In this context, "increment" or "iteration" refer to making relatively small changes to a program before rebuilding or redeploying it. One of the core ideas of agile is that you want to aim for frequent, rapid iterations.
In agile you typically want the program to be buildable and shippable at all times. It may not be terribly useful or feature-complete for a while, but you always want it to be a thing you can actually build and ship right away so that people can start testing it and giving feedback (as opposed to the "waterfall" approach where no one can really try it out until the whole thing is finished). Then you add features to it one at a time, though each one may take anywhere from a day to a couple of weeks or maybe even months.
In many places each increment/iteration is the release made at the end of a "sprint", i.e. a period of 1-2 weeks associated with a short list of tasks the team aims to get done in that time.