Fly-fishing reels are used to hold the line and are not part of the casting process. You strip line from the reel and it lies at your feet while casting, feeding out when you need it. This loose line is controlled by your free hand while your other hand holding the rod makes the cast. You don't touch the reel while casting with a fly-fishing outfit.
A fly-fishing reel.
For most freshwater fishing, fly-fishing reels are not as important as they are in most other kinds of fishing, because retrieving line and fighting the fish are done with your hand. Line is stripped in with your free hand and that hand controls drag when setting the hook and fighting a fish. This is not true when fighting strong saltwater fish or freshwater fish that make long runs. With them, the drag on a fly-fishing reel becomes important just like on other reels. Special fly-fishing reels are made with good drag systems for fighting big-game saltwater fish and freshwater fish like steelhead. You fight them by controlling the line with your hand for the few seconds it takes them to pull all the slack out; then you start fighting them with the reel just as you would with other kinds of reels.
There are two kinds of fly reels, manual and spring loaded. With the manual reel, a handle is either attached directly to the line spool or moves it through a drag system. You reel line in by turning the handle. With the spring-loaded reel, you wind up the spring and the spring turns the spool when activated with a lever in front of the reel. This spring also acts as a drag system, but it's limited.