What Happens After Bottling
The most important thing that's happening in that bottle right now is that you're beer is carbonating. The yeast is eating the last bit of sugar you added during bottling and releasing carbon dioxide. The carbon dioxide will first float to the top of the bottle, and then, as that space gets crowded, it will be gradually forced back into the beer itself. This is how carbonation works (science!) and why you see streaming bubbles all the way through the liquid once you pull off the cap.
This carbonation process takes between seven and 14 days, depending on factors like room temperature, active yeast left in your beer, the kind of sugar you used to prime the beer, and a few other things. It's not an exact science, which is why I generally recommend waiting a full two weeks before sampling your beer.
In addition to carbonating, your beer is continuing to clear and condition. As they finish consuming the priming sugar, the last yeast will fall out of suspension and collect on the bottom of your bottle, along with any other leftover solid bits that haven't cleared yet. This little bit of trub is unavoidable in homebrews — it won't generally affect the flavor of the beer unless there's more than a quarter-inch of it (usually it's just a very thin layer).
Beers also sometimes go through a bit of bottle shock when they're first bottled. If you taste the beer early, you might pick up some harsh notes or sulphuric flavors; these dissipate after about two weeks in the bottle.
The flavor of the beer also keeps changing — and will actually continue to change (usually for the better!) over the months to come. You might notice that your beer tastes different two months from now than it did when you first tried it. With most beer styles, I actually find that the flavor continues to improve over the months, and then starts to deteriorate after a year.