Analysis is one of the largest divisions of modern mathematics (Algebra, Geometry, Topology, are some others).
Analysis is the study of limits. Anything in mathematics which has limits in it uses ideas of analysis. As you know from calculus, limits are the basis of understanding integration and differentiation, and, as you also know from calculus, these things are the basis of everything in the world you could ever need to know.
Probably, when you took calculus, you spent a lot of time learning techniques of how to integrate and differentiate, and actually learning about limits was dealt with in a fairly short time. But limits are a very rich, and very subtle concept. So, if you like, you can think of a theme in this course as “lift up the hood of calculus and take a look at what’s inside”. But you’ll also find a lot of ideas that are completely new, and that are tied in with thinking about what we mean by a limit.