Ok, seems like a lot of folks are not answering this part of the question well… what are the codes for…
There are the codes that mean emergency, as others have listed… And there is the standard (in U.S. 1200 which is a VFR flight operating outside of a an airport controlled area (Bravo, Charlie or Delta).
However, if you are IFR you’ll be assigned a code. And if you are VFR in radar controlled space (bravo, charlie or delta) you’ll most likely be assigned a code.
The code is any group of 4 numbers (excluding the reserved emergency numbers). So for instance upon initial contact with a controller they may assign you a code, lets say 4345… You dial that into your transponder, when you do, the radar at their location now can tell which blip on the screen is actually YOU because it will return that code… They can then cross reference that with your aircraft data – I believe they still call this a ‘tag’ in ATC lingo. Your tag contains all the relevant info… Aircraft type, registration or call sign, and in mode C (altitude reporting transponder) it will contain your altitude.
So now, when the controller looks at your blip, he knows exactly who you are, where you are going and what alt you’re at.
the IDENT button on your side is used only if the controller requests you to IDENT, you tap that button and your blip on his screen will momentarily get brighter. This is used to draw his attention to your blip… Can be a real time saver if he’s got 15 blips on his screen, rather than looking for the one that changed, he’ll see you light up and gives him a quick idea which one is you.
Thats the shorthand laypersons version of what it does. Hope that helps.
(EDIT) – I should add that the emergency codes will generally cause your tag to light up RED on the radar screen to indicate some sort of emergency and help the controller know you have an issue… For instance no-radios, hijack, etc… You MUST be very careful in real world to never even roll past an emergency value, because even if it is in there momentarily you might light up on the controllers station and cause a bit of a scare.