Perennials make a garden come alive by the way they grow and change with the seasons, they are never static.
Majority of perennials go into a dormant phase over winter - they are not dead, merely bunking down and waiting for the weather to warm again come spring. For some perennials this means all you see is a clump of foliage, for others there may be nothing to see above ground. Come spring, growth starts to speed up and as summer approaches things are well underway.
Majority of perennials get on just fine without our help but to maintain a longer display, removal of the finished flowers does help encourage more blooms. As the perennials come to the end of their flowering time some gardeners like to tidy everything up, others wait, leaving the seed heads and stalks to provide interest over winter before tidying up in early spring. In very cold climates leaving the foliage/stalks intact may provide further protection from the cold for the plants.
The joy with perennials is being able to propagate more plants - as the plant becomes established it gets bigger, then you can divide it up to make more plants! Usually this is done in spring as the weather warms or for plants that have finished flowering it can be done in autumn so the plant can then establish itself before the ground chills or freezes or in my case turns into mud!