There are a number of ways of defining sociology, especially as sociology is a very broad discipline. However, here is a short definition.
Sociology is the study of social relationships and social institutions. Sociology's subject matter is also diverse. For example, sociologists study subject matters as diverse as religion, crime, family relationships, racial interactions, gender, revolutions, formation of groups, knowledge and so much more.
What unifies all of these topics is the desire to understand how humans both shape and are shaped by surrounding cultural and social structures.
Perhaps a concrete example would be helpful at this point. One of my favorite sociologist is Peter Berger. One of the things he studies is the sociology of knowledge. In one of his penetrating books, he argues that all reality is socially constructed. By this he means that that the objective features of the world have assumed their shape by people. Therefore, what seems like a given or simply objective is actually created by people. The implications of this are great such as in his theory of plausibility structures. What is plausible in one culture is different than what is plausible in another.
In conclusion, sociology is not only a broad discipline, but it can also be very helpful in understanding the world.