What is an example of an abelian group?

Could you provide an example of an abelian group, perhaps with a clear explanation of its properties? It would be helpful to understand how the elements of this group interact with each other under the operation defined, and why this group is considered to be abelian in nature. By breaking it down in this way, it may be easier for those who are new to the concept to grasp the fundamental principles of abelian groups.