It means nothing more than 「びっくりした」 or just 「びっくり」.
「びっくりぽん」 is a phrase used often by the main character あさ for あさが来た, an NHK morning drama. This program has been in existence for decades now and it is extremely influential in the Japanese show biz. The main character is always a girl/woman and the actress who is selected to play it often becomes successful later on.
Anyone who is studying Japanese would know how much we love using onomatopoeias. In this case, a fairly random 「ポン」 is just attached to the existing phrase 「びっくり」. To me, 「びっくりぽん」 sounds quite lively, light-hearted, full of pep, etc. It sounds very catchy indeed.
I have expalined this at least twice before without much success, but the word 「びっくり」 itself is highly onomatopoeic to begin with. You will keep encountering "four-letter words" in the form of 「〇っ〇〇」 (second letter is the small っ). Most of these words are adverbs and many are onomatopoeic as well. So, 「びっくりぽん」, to me, is double-onomatopoeic and that means it could be expected to become popular in this nation of 130-million onomatopoeia lovers. It's like a double cheeseburger for Americans!
In the following video, none other than actress 波瑠{はる} herself (yes, she has a short name), who played あさ talks about the phrase in question in a talk show.
https://www.youtube.com/watch?v=rr1_3c2L7tg
Around 0:15, catch her say 「どこから来{き}たんでしょうね?」("I wonder where it (the phrase) comes from.") If 波瑠 doesn't know, there is no way you or I could know.