I am a beginner with set theory.
What is meant by " analytic set " ?
I see this term in the context of set theory, calculus and real analysis but I have no idea what it means.
See here : https://en.wikipedia.org/wiki/Borel_set
where it occurs in the non-Borel set part.
At the first you should know about Polish space; by knowing topology and having a general knowledge about it, we can explain like this:
polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset.
Common examples of Polish spaces are the real line, any separable Banach space, the Cantor space, and the Baire space.
Now we can say, subset of a Polish space $X$ is an analytical set if it is a continuous image of a Polish space. for giving you more information I will link Wikipedia and Youtube. https://en.m.wikipedia.org/wiki/Analytic_set
https://youtu.be/xX7ORlPu5xE?si=6C1yqGGNPnrsW8sN