In mathematics, a group is a set of numbers or objects (like shapes) that you can do things with. Think of a group like a team in sports. Everyone on the team has to work together - the same is true with a group in math.
For example, let's say you have a group of numbers - 1,2,3 and 4. The way the group works is that when you combine any two of these numbers using a special math rule (like addition, multiplication, etc.), the result should also be part of the group. So when you add 1 and 2, you get 3 which is part of the group - this means this group follows the special math rule!
Groups are important in math because they make it easier to solve a lot of problems.