One of the principles which the LaTeX kernel, and many of the packages outside the kernel, attempt to follow is that documents should look the same (even up to spacing behaviour) when they recompiled on different machines with different package versions, even decades apart.
pgfplots is a regularly updated package that frequently adds new features and fixes bugs. This also means that some old documents might look different if recompiled with those new features/bug fixes enabled. Hence pgfplots provides a feature whereby you have to explicitly request which version of the package you want to use (or at least essentially, as the package provides backwards compatibility emulation for older versions), and hence which new features and bug fixes you want access to.
This is a "good thing", but it explains your warning - you are not using all the features and bug fixes available to you. Some of the fixes include better placement of tick labels, as mentioned in the warning. This is not enabled by default as it would clearly change how existing documents appear.
Section 2.2 "Upgrade remarks" of the pgfplots manual discusses this.
For completeness, I provide information on selecting the version:
Requesting a specific version
To request a specific version, just use the compat option:
\usepackage{pgfplots}
\pgfplotsset{compat=1.7}
The bleeding edge (discouraged)
You may be happy to live on "the bleeding edge" and to always use the most recent bug fixes etc that pgfplots provides. pgfplots also allows you to specify this, but encourages you not to as your document may compile differently before/after updating the package at certain times, and you may not be explicitly aware of the changes or what has caused them.
Hence, if you choose to select the newest version with
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
then pgfplots still issues a message (not a warning) to remind you, which you might miss:
Package pgfplots notification 'compat/show suggested version=true': document has been generated with the most recent feature set (\pgfplotsset{compat=1.7}).
This notification can also be disabled:
\usepackage{pgfplots}
\pgfplotsset{compat=newest,compat/show suggested version=false}
Remember though that the pgfplots author discourages this! Again, see the manual for the offical information.
pgfplotsmanual doesn't help you, then I'm not sure I can either. The only timepgfplotsguesses a version is when you requestcompat=newestand it tries to estimate which new features you are using and which you are not, to encourage you to request a specific version instead ofnewest. There have been some bugfixes etc that have not preserved compatibility, so loadingcompat=Xmay not be the same as loading versionXof the package file as it was when released. For more help, I suggest that you start a new question with a MWE where someone more knowledgeable may find it. – cyberSingularity Jun 26 '14 at 13:35compat=Xand I obviously got the same warning asker did. Maybe my question should be: what version exactly (or what middleground/approach) is used in "backwards compatibility mode" when you don't specify anything, and on what basis does pgf suggest "usecompat=X" (eg asker got X=1.6 and I got X=1.9) – nathdwek Jun 26 '14 at 13:48compatthen you getcompat=defaultwhich is the same aspre 1.3. Obviouslypgfplotscannot suggest a version newer than the version of thepgfplotspackage that is installed, but I don't know the specifics of howpgfplotssuggests a version. Perhaps if there have been important bugfixes, it suggests newer versions even if it hasn't detected use of certain new features. If you want your document to look close to how it used to look, then find the date of the old document and try the latestpgfplotsversion that was available then! – cyberSingularity Jun 26 '14 at 14:0514 > 9 > 7, hence1.14 > 1.9 > 1.7. Does that help? It's just a case of the leading zeros being implicit (1.7 = 1.07etc). – cyberSingularity Dec 10 '16 at 09:29