Cycling can help you play your terminals more often, but they're not the only way to do so. As TheExpressicist mentioned, you can just buy more terminals. Also, you can just buy a load of Schemes, but Scheme isn't really a cycling card.
Cellar, Warehouse, Inn: These cards all reduce your handsize by one. Using them to cycle early on often comes at a cost of not being able to afford as much.
What does cycling really do? Look at Chancellor. Chancellor doesn't help you play your purchases more often if you discard them with it, but it does let you play your new purchases sooner. This is the real effect of cycling: finding your new purchases sooner. This is good while building up, but can be bad when buying VP cards. Garden rushes with Workshop are a prime example of when you don't want to cycle. In that case, cycling leads to more Gardens clogging your hands. There too, you play thr key terminal, Workshop, as often as possible by gaining a lots of them.
Now, there is also the idea of filtering, or sifting as often referred to here on the forum. That's when you are able to, uh, exchange cards you don't want to draw with cards you do want to draw. This corresponds to when your cyclers are discarding junk cards like estates and curses. Having large handsizes increases the chance that your cyclers/sifters like cellar will have junk to discard. If you trashed all your junk, then sifters aren't so useful, and their hand reduction will work against you.
Early game, cellar has some issues. Imagine a hand of 4 Copper and 1 Cellar, with 3 Estates on top. Discarding your copper will give you a hand full of Estates, killing your current turn purchase. Warehouse, however, could have drawn and discarded those estates, improving your next turn without weakening the current turn too much. This is its key advantage over Cellar, and its because it sifted better than Cellar. Cellar would have cycled as much though.
So yeah, cycling and sifting: subtle but valuable differences.