The wheel can appear when you are downloading something, trying to operate a program that is CPU intensive, or when your computer is working through an operation. The spinning wheel indicates common issues such as when a program is performing some sort of action that is in progress, when demanding computing tasks are taking place, or when a Mac is frozen altogether.
This is not a symbol unique to Mac computers, though their multi-colored wheel is well known among Apple users. It sounds comical but if you have experience with one, you know that it means an issue might be lurking inside your computer.
The spinning wheel may be known by many different names but what it actually is a system indicator that is technically called a throbber.