Yes, you've got the idea. It stands for Portable Game Notation and is a format for saving chess games on a computer. If you have a chess program that can load chess games, chances are it accepts .png. It is pretty standard.
PGN - what is it?

Forsyth Edwards Notation - another format for saving chess though this is commonly used for saving the position of all the pieces at a given point in the game so that the game can be analysed/restarted etc.

FEN is based on a system developed by the journalist, David Forsyth. FEN is an integral part of the PGN for chess games, since FEN is used to define initial positions other than the standard one. FEN does not represent sufficient information to decide on draws by repetion of moves , for that, a different format such as EPD ie Extended Position Description is needed.
I'm just wondering what the PGN button does at the bottom of the recent games list. I've worked out that it contains the game moves or something similar, but I don't know how to view it in a program or what type of program will run it. Any insight would be great!