Eventually you'll start wanting to say more than 'put this movieclip on the screen and move it'.
Such as 'place a new tank X where factory Y is, have it walk one tile right, and set both inactive for the turn', or 'list me all mobile enemy units between tiles X and Y'.
When you build bigger games (than miserable platformers driven by a few hittests), you certainly want to have these abstractions, that you could use to talk about tanks and tiles, rather than just have some movieclips with their limited functions.
Object orientation is a concept used everywhere for building such abstractions, so that your programs are more to the point and overviewable, rather than what you'd get if you started building it by writing a loop that makes the tanks chug when they're idle.
Of course, to use OO you need insight in advance of the program units that you'll need, which makes it difficult for the kind of schmucks on this forum.
Now more technically, the way AS3 works uses classes intrinsically and you're using them even if you're not aware, as Flash translates code on every timeline into a class, each symbol has a class. So you might find what you're doing currently is similar to what classes are for, and that there's nothing much fancy to classes.