Linguistics is the scientific study of language. As a linguistics student, you become adept at noticing what people say, aware of the unconscious choices implicit in this, and able to provide a rigorous explanation of how such choices are made. The field encompasses questions such as these:
Linguistics is one of the principal areas of cognitive science, and is closely allied with many other fields of study, including cognitive psychology, speech and language pathology, the social sciences, education, computer science, philosophy, and the study of particular languages.
What linguistics emphatically is not is simply the study of many languages. A person who knows many languages is a polyglot, not a linguist.