I just signed up for a Composition Challenge on this forum (link) and I had a question on how to do something.

In the "Basic" requirements, it asked to include "A Simple Structure" in the song. Is this refering to the time signature, or are there actually different names for structures that I should know about.

If there are different types of structures, how would I learn about them?
There are many different structures. Many of which you shouldn't worry about if you're in the beginner stage of theory.

What it's referring to is the way the song is arranged. Verse - Chorus - Verse - Bridge - Chorus is a very common and simple structure (Give or take a few verse's/chorus'). The 12-Bar Blues is a very common and simple structure as well.
Most popular songs on the radio are usually:

Quote by Demonhunter04
You are my hero nodurquack.