A social group is any group of people that interacts socially - socially just means here "with others".
Some social groups are small - friends - and some are really big - a nation.
They are important to society, because in a way they are the society itself - its different parts. It forms the basis for the society's interactions, for example the raising of children happens within a family - which is a social group.
You are part of many social groups, for example: your family, your classroom,your school and your nation