PPA means “personal package archive” and it’s exactly what the name says: a repository of .deb packages for some Ubuntu version(s).
It’s a very convenient way to make packages available to other people: you submit the source package and a pool of virtual machines build the packages for different architectures (i386, amd64 and lpia; the ones supported by Ubuntu).
Canonical launched PPAs in the summer of 2007 in beta. I can’t remember when I joined the program but I immediately loved it: it made very easy for me to make packages available for several machines in several different locations. Easier than carrying a USB pendrive.
My PPA has had packages for virtually every version since Dapper but due to disk-space restrictions, I had to remove everything but Hardy and Jaunty.
What can you find in my PPA? A lot of stuff, really. What people tend to thank me the most for? Recent (meaning “usually the latest one”) versions of Firefox, git, Samba, CMake, Boost, Qt, glib and gtk, Wt, Valgrind, Pango, Doxygen, GStreamer, asciidoc, KDevelop4, QtCreator, the NVidia graphics driver, OpenVPN, Subversion, VLC and some other packages (even Open Cobol ðŸ™‚ ).
Generally, the same packages are available in the same version for all the distributions I’m “supporting” (keep in mind this is a best-effort repository: I can’t and won’t offer any warranty!). From time to time, it’s just too difficult to backport something (it requires too many dependencies to be backported too) or there are technical limtations (for instance, recent versions of VLC won’t build on kernel 2.6.24, which is the default kernel on Hardy, so the latest VLC for Hardy in my PPA is 0.9.4 -Hardy came with 0.8.6-)