I think of it as layering flavours.
Assuming a 60 minute boil, hops added at the start will have their volatile compounds (generally the ones with the fruity/floral flavours) driven off by the boil. That will leave you with the isomerised alpha acids and the less volatile compounds. Terms like herbal and dank get used often to describe the flavours these compounds contribute. This depends on the hop, some will contribute very little flavour wise and come across as clean, others will leave some flavour. Whatever hop, though, at 60 minutes or more the contribution is pretty subtle.
Going to the other end of the hot side, post boil additions will give you more of the volatile compounds in your wort. Even within the post boil additions you can fiddle with the wort temperature and length of hopping to favour the volatile compounds versus the less volatile compounds. Add the hops as soon as you turn off the heat and you're still going to drive off a fair percentage of those volatiles. Turn off the heat and drop the temperature to 80C or a bit lower before you add the hops and you're not going to drive off as much.
Then going backwards from the post boil additions to the other boil additions people use they will contribute more of the various compounds in the hops the closer they are to the end of the boil. And the closer to the end of the boil, the more they favour those more volatile compounds.
Then on the dry hop side it happens all again. Temperature and time can be used here to capture more or less of the various compounds, depending on what you want. Longer dry hops give more opportunity for the less volatile compounds to dissolve into the beer and the volatile compounds to be expelled by fermentation. Lower temperatures don't seem to affect the dissolution of the volatile compounds, but slow down the less volatile compounds. So if you wanted to favour the newer hops with the fruit notes you'd do a shorter hop at lower temperatures. But if you wanted a mouth puckering dank bomb you'd not worry about the temperature and dry hop for longer.
And all of this also depends on the particular hop. Some will be close to useless at one or two points in all the possible hopping points. I find a lot don't contribute much to the post boil hot side additions, while others really shine through there. Some will contribute quite a bit when added early in the boil and next to nothing in a dry hop. That's just experience, or asking others, or reading the increasing number of blogs looking at the chemistry of hops -
http://scottjanish.com/survivables-unpacking-hot-side-hop-flavor/.
That's not to say that the current trend of adding a clean bitter hop at the start of the boil, or nothing during the boil, then loading up with post boil and dry hops additions is the only way forward. It's just the current fashion. Fashion changes and I'm sure it's not far away when we all get overexposed to the same way of hopping beers and look for something new or swing back to the West Coast approaches. So, for me, it's a matter of working out what I want for the beer.
So for two examples...
I love a crushable, blonde 4% ABV hoppy ale. For those I follow the current trend, a tiny bit of Magnum at 60 minutes, a bunch of the latest generation hops post boil at 80C and then a decent dry hop. Then for variety I play around with yeasts, cali ale, saison and I've got plans for playing with brett as the primary.
I also love a black IPA (I noticed they had a revival down here this winter, there were nearly a dozen different breweries doing them). For those I add something at 60 minutes, something at 30, something at 10 and then a dry hop. I just find a lot of the post boil hot side hop flavours are overwhelmed by my grist (my black IPA must have some roast flavour, screw the style guide). So I skip them.
So if you've got a hop flavour profile you're going for we can all chip in and see if we can confuse you.
