What is the use of culture?

I generate Culture with Amphitheatre and Temple.

But what is the use of it? Does it add Happiness of my kittens?

Culture's primary use is in making manuscripts out of parchment. Manuscripts are needed to research some early game technologies, to make temples, and then can be crafted again (with science) into compendiums, needed for mid-game technologies. Even once you've finished those, the compendiums can be crafted again (also with science) to become a more reliable source of blueprints, for late game technologies as well as for making machines like Steamworks.

Culture is just a resource like any other. For example, making manuscripts requires 400 culture.

Also, finding the Naga tribe requires having 1500 culture at the time you send out explorers.