The answer is both simple and complex. The simple answer is that the hops will give your beer different flavors and aromas depending upon when you put them in. Earlier additions will result in more bitterness, but generally less hop flavor and aroma. Additions around the 20 minute mark or so (that is 20 minutes remaining in the boil...the standard way of expressing hops additions) will give you more hoppy flavor, but not as much aroma and much less bitterness, and later additions will give you more aroma but less flavor and very little in the way of bitterness.
Dry hopping doesn't really add much in the way of bitterness. In my opinion it can substantially add to perceived bitterness, but generally speaking when you add dry hops, you are going to get a much more hoppy aroma which can have a big impact on your beer.
I've got this chart, which I shamelessly stole from somewhere else and cannot properly give credit, which shows how the amount of time you boil the hops influences the hop profile of your beer:
There are some sort of exceptions to what I just said, as you can get interesting effects by using first wort hops, for example, and hopping in the mash, but the trends in the chart are pretty accurate.