Anxiety is a physical and mental phenomena usually characterized by worry and physical sensations (e.g., increased heart rate, muscle tension) triggered by perceived danger. It is very similar to fear in that your body is preparing for fight or flight, but there is no concrete, imminent threat (e.g., a lion charging or a car heading towards you) with Anxiety.
Everyone experiences anxiety at certain times (e.g., giving a speech, school exams, job interview, etc.). It becomes problematic when it is frequent and/or intense and affects the quality of your life. Anxiety can also trigger various compensatory behaviors to reduce this unpleasant feeling such as avoidance of certain situations or self-medicating (e.g, alcohol or drugs).
Anxiety can have a genetic component from your parents. It also can be triggered by various life events such as your upbringing, negative social interactions or traumatic events.