As it should have been implied, osu! is a rhythm game, with four different game modes -- Standard (std), osu!taiko, osu!catch ( ctb / Catch the Beat ), and osu!mania.
In osu!standard, or the default game mode, you may click circles and hold+drag "sliders", and at some points, even spin in circles!
One element of the game is, well, obviously -- rhythm. "Beatmaps", or levels created by users, are designed to follow the rhythm of their songs, so you will find yourself clicking to the beat of the song.
You have the option to play in different ways -- you can decide to be one of many different types of playstyles:
> Mouse-only (aiming and clicking using only the mouse) > Mouse-Keyboard (aiming with the mouse, tapping the "Z" and "X" keys to click) > Pen-only (Using a drawing tablet as a mousepad of sorts and using the pen to aim and click) > Pen-Keyboard (Using the pen to aim, and the Z and X keys to click) > Trackpad-only (aiming and clicking with only the trackpad, if you're playing this on a laptop) > Trackpad-Keyboard (aiming with the trackpad, clicking with Z and X)
I may have not described as well as many others would, but I hope this helps! Good luck on your journey of mastering osu!