I have noticed that after I disconnect my battery to do some work, my car has a rough idle for a couple days before it mellows out. Has anyone else noticed this phenomenon? Can someone explain why this happens? I figure it has something to do with the computer adjusting setting or something. But a detailed explanation would be great.

You answered it yourself. In fuel injected vehicles which are managed by some sort of computer (ECM) also have a memory in that computer. The memory doesnt require much power from the battery to be functional. Its about the amount of an LED.

As you drive or run your vehicle, it sort of "learns" its characteristics. I will go so far as to say, it learns your "style" of driving, and adjusts the engine to run optimally via fuel air ratio and various other things depending on the vehicle.

When you disconnect the battery it loses this memory, so when you start the car again, it has to "relearn idle". Takes a little while depending on the car o smooth out. Could take a couple of hours to a couple of days.

Im not sure HOW it learns, or what exactly it does after its learned the characteristics, but thats the gist of it.

You can get a 9-volt battery adapter that plugs into the cigarette lighter that will keep the computer memory intact while the battery cable is disconnected. Keeps your stereo settings, too.

I wonder how it "learns", how fast it learns, and what information it actually uses to make adjustments.
Could this depend on the condition of the engine and components? For example, if my engine is in poor condition (sensors and components) will it take longer to adjust as the ECM tries to smooth everything out?