Basically, Cinch does what all great Mac software does: it works in the background and lets you do what you want to do, skipping completely all the usual nonsense you usually have to do in between. Basically, it's a window helper -- all you have to do is drag any window on your desktop to a side of the screen, and it'll put the window maximized in that space. Drag it to the top, and it'll maximize it across the screen. When you're done, drag the window away, and it returns to its original size.
There's a great screencast on the Irradiated Software website that shows some of the possibilities. One idea that really appeals to me is dragging two Finder windows quickly to either side of the screen to both browse two folders at the same time, and then pass files back and forth between them.
Cinch reminds me of this old chat by Quicksilver creator Nicholas Jitkoff, where he talked about software that didn't worry about what you wanted to do and just let you do. Cinch serves its purpose in that same way. It's available over on the website for US$7.