All plants have a cycle. It really isn't unlike us people, just on a different scale. We start out juvenile, we grow to sexual maturity, we reproduce, then, well, you know.
Plants are just the same. Annuals which die after only one year spend the majority of their time in their "sexual maturity" stage. They simply flower, and flower, and flower. Their signle goal in life is to reproduce. If you pluck the flowers off before they go to seed, some plants like geraniums and verbenas will just keep flowering. Others, self-clean themselves and just keep on flowering to reproduce as much as they can before they die off.
Perennials, on the other hand, have a slightly different cycle. They do have a juvenile stage, but us greenhouse growers usually take care of that stage. But in your garden, they have a growing, flowering, and fruiting stage (fruiting means producing seed, not fruit as in what's in the fridge). The order of these stages can vary. The growing period can come before, after, or even before and after the flowering cycle. Fruiting always follows flowering so we'll just treat them as one stage. By leveraging these different characteristics, you can extend the season and vary your garden to have flowers the entire growing season.
For example, early flowering creeping Phlox (Phlox subulata) flowers really early in the spring and then grows the rest of the summer and fall to prepare the the next spring. Summer Phlox, on the other hand, grows in the spring, produces flowers in the summer, then grows a bit more in the fall until frost hits. Black Eyed Susans (Rudbeckia fulgida) grows in the spring, then flowers late summer and into the fall.
Now there are a few exceptions that flower through the season, but those are pretty rare and their "continuous" flowers aren't always spectacular. Often times you'll get one bit burst of flowers, then little bits and pieces thereafter.
Another advantage with some perennials is the foliage or leaf texture and/or colours. Perennials like Foamflower (Heuchera spp.) or Hostas do flower, but the majority of their interest in the garden is actually their coloured leaves. The flowers are just a bonus.
Essentially, that is the formula for the all-season perennial garden. Some spring flowering perennials, some summer flowering ones, and some fall flowering ones with some splashes of foliage plants thrown in for good measure. Of course, it may somewhat of an over-simplification, but that's really what it boils down to. See, gardening isn't that hard after all.