This talk has two goals. The first is to tell you what a cluster algebra is; broadly, it's a type of commutative ring that encodes "local moves" in various combinatorial objects. The second is to convince you that cluster algebras are beautiful and natural to consider. I'll give plenty of concrete examples, including cluster algebras from surfaces and Grassmannian coordinate rings, to motivate the definitions and theory. Beyond combinatorics, cluster algebras do have applications to e.g. quiver representations, homotopy theory, Diophantine equations, Poisson geometry, and discrete integrable systems, but I won't talk about any of those.