At its core, economics is the study of choice?why choices need to be made, how choices are made, and the implications of those choices for quality of life.
The breadth of this description gives you some indication of the breadth of the discipline. Economic questions enter into all aspects of social life?how wages are determined, whether taxes should be raised, how to best provide equality of opportunity in society, how to protect the environment, how to get rich, or how to use resources to satisfy needs (this is only a short list of the many avenues of economic exploration).
If any of these issues are of interest to you, economics is relevant to you.
How do economists explore these questions? Through the development and empirical testing of economic models. These models apply mathematical abstractions to the "real world" so that economic statements may be made precise.
This precision points to the key reason that economists are valued by the business and public policy communities?precision helps avoid foolish (and expensive) mistakes. It also explains why economics is a "hot major!"