Our group meets once a month for a long 8–10 hour session. There is always the moment at around 6–7 pm where we like to have dinner together. We have always just taken a break and came back to the game after we finish eating, but I am tempted to try and incorporate this in the story, so that we can stay in character.
How can we incorporate a meal into the game play constructively? That is, without it feeling forced or pointless?
I'm going to take a radical position and suggest that eight hours is a long time to roleplay without a break from playing a role in any case, and that the meal-as-a-break may actually be a welcome respite for some players.
For some people roleplaying can actually be hard mental work (or for some kinds of people it can be mildly stressful, if enjoyable); there's a tendency after a couple of hours to start falling out of character or getting involved in side chats as fatigue hits. A break - including a meal - can be a useful place to defer that to ("stay in character guys, we'll break in half an hour").
As a player perhaps it would be pleasant but not essential -- but if I GM I'd find the break very welcome, and if I was continuing to GM while trying to eat it would be hard to focus on enjoying the food, with so much to keep in my head.
On special occasions the meal could be part of the roleplaying, but I'd suggest that most of the time you just take a break and eat.
In the last group I played with regularly, we often ate (and had a break) in the middle of a long roleplaying session; it was one of my favorite parts actually. One thing we would sometimes do while eating is discuss some of the more mundane aspects of the game - more mechanical or account-keeping details of the game that didn't involve roleplaying or combat for example - where it wasn't necessary to stay in character. The GM could still be GM in the sense of being the arbiter of how things work - but without the effort of keeping the current "picture" of everything straight or of playing any roles at all.
Your meal break should be taking place when the PCs themselves are sitting down for a meal. This should keep you guys in the roleplaying mood without necessarily breaking your immersion. Its as if your PCs are opening their packs of Trail Rations (See:McDonalds) and digging into the dried meat treasures (See:Hamburgers) that lie within.
I'd also recommend that you guys pick up your meals before your game starts instead of after so it isn't nonconstructive to your play time. A food run can take as much as 30 minutes if you include the actual eating, if you pick it up on the way to the game before the game actually starts and stow it in a fridge you can heat it up when you begin camping, resting at an inn, etc.
After all, your PCs eat three times a day just like everyone else.
Back when I was still doing mammoth sessions with my main group we used to routinely do snacks and meals without seriously impacting the game. The fact that the players are sitting there munching on Doritos and Dominos (the other D&D :P) was no more relevant to the game than the fact that we were rolling dice instead of actually swinging swords, or that the Barbarian's player just had to go to the toilet in a hurry.
Immersion is great and all, but there's only so far you can take it before you stop roleplaying and start play acting.
As for the mechanics of how you go about fitting the meal in, there are lots of ways that you can free up a player or two if someone needs to go make a food run. A lot of our sessions included points where one or more of the characters were involved in an event that didn't include the rest of the party, which is an ideal moment to duck out to call the pizza place or even hit the drive-through if the episode is a long one. You might miss a few details that your character wasn't privy to anyway, just clear it with the GM and the group before you take off.
Another option, if getting away from the gaming table is required, is to plan a section of the game that doesn't need props and such. We spend a lot of time just talking, might as well do that at the dinner table as anywhere else. How well this works is going to depend on the group and the nature of the adventure of course. Not every game situation lends itself to a half hour of sitting around just yakking, and you should always keep a few dice handy for some ad-hoc decision making, but if you plan a low-key interaction over that time and make sure the players don't decide to launch a new combat with the enemy army over the hill, you might be OK.
Or, if all else fails, night time when everyone (except the poor sucker on watch) is asleep is probably a good time to pause and take time out for a meal. Then you can surprise them with a midnight encounter when you're all feeling nicely sleepy from that impending food coma.
From experience though, I have one suggestion to make: make sure you have plenty of paper towels or similar around so that nobody touches a character sheet, prop or die with hands covered in pizza grease or chip crumbs. Bad enough that we can't keep these things safe from the occasional beverage incident, don't let food on them as well :P
I'm going to take the approach that the meal would be completely in-character or in-game while still being enjoyable for this answer. Roleplaying a meal is something that I would not do all or even most of the time, but it's an idea that can definitely add some variety to your campaign.
If you want to make it an important scene, a meal scene in the story is traditionally used to show the characters sharing with each other, and to show relationship status. It is obviously a good time for some light character interaction.
Besides that, communion was (and still is) seen as a sacred thing in much of Western and especially Christian culture. Breaking this communion is a dire omen and a sure sign of bad things to come. However, a completed communion is a good omen for all parties involved. If your game is narrative-focused, you can use this opportunity for some foreshadowing. I recommend that you don't parallel any interrupted communions by flipping your own table over and spilling everyone's food, though. I would probably just wait until everyone's done eating out-of-character and then continue from there.
If you want to use a meal scene as an important plot scene, I would approach it from the angle that the meal is just the backdrop for your scene. The point of the scene would be that your party needs to talk to NPC A because they are the duke of Region B, not that your guys are hungry. But you can use the symbolism I was talking about in the paragraph above during the scene -- that's what makes the meal matter.
If the party is travelling at the time you happen to break for a meal, you can use that time to talk more about the surrounding area the party has been travelling through, or answer any other questions about the world your campaign is set in. This doesn't necessarily need to happen in-character, since there isn't necessarily any NPCs to role-play with, but it's providing information that will help the players out with the game and hopefully provide them enjoyment if they're curious. You can also use the classic tavern setting when you're in town to provide a useful in-game backdrop where the players can seek some information without putting forth much effort (which is lacking during a meal). Heck, it might even be fun for you to describe what the characters are eating, depending on the local area.
When hosting long gaming sessions like this and still trying to stay away from delivery food, I've found that crock pots come in very handy. A nicely-thought-out stew or roast could easily be adapted to your game world if desired and is exceedingly simple to serve. Combine it with a spread of meat and cheese or some finger sandwiches if you need a little more variety or options for pairing with your particular scotch.
The above options also have the benefit of being less messy than things like pizza or fast food (unless you have very messy guests, in which case all hope is lost anyways).
I agree with those that are advising to keep it as a break, especially if the session is that long, but whether you're in-character or not it's still fun to have a themed meal for the game, or at least something nicer than fast food. A hands-off cooking technique like a crock pot or something that can be prepared in advance like a cheese tray are essential to minimizing the impact on play time. I know from experience if you're playing that long and get interrupted for too long of a break, it's hard to get back into the game again (the moment someone flips on a TV you're doomed).
Many game worlds even have enough of a community that someone out there has developed recipes for them, so you could dig around online a little to see what there is.
