I have found that many people are not sure what "anxiety" is, exactly. Anxiety refers to an inner state that can range from feeling nervous and unsettled, to a state of panic. Anxiety can feel like fear, but whereas fear is a specific reaction to a realistic threat of some kind, anxiety is either an irrational response to a stressor (which can include our thoughts), or even a state that exists independent of any apparent stressors. Symptoms can include: feelings of dread and uneasiness, physical sensations of "electrification" or feeling "wired" and/or immobility and "shutting down," excessive worry, restlessness, fatigue, problems in concentration, and muscular tension.
Anxiety can be in reaction to very specific stressors, situations or environments, or it can be "generalized", meaning it is felt most or all of the time, and/or across a wide variety of situations and environments. What we call "anxiety" is generally a feeling that is strong enough that it interferes with our mental clarity, our sense of well-being and our ability to deal with situations and stressors; when anxiety is strong enough it can drive us to focus primarily on finding some way to calm the feeling, rather than successfully addressing a situation, or correcting a problem. Unfortunately, when we feel anxiety we can often feel driven to look for ways to escape it (avoiding what triggers it, using substances such as drugs or alcohol to numb the feeling, developing compulsive patterns of behaviour, etc.) This can then evolve into developing "anxiety about feeling anxiety."
Like Depression, the medical model tends to see Anxiety as a mental illness; as with depression, I find it more useful to look at it, and to treat it, as a symptom. Anxiety is usually related to patterns of thinking, beliefs, and how we learned to feel and to see ourselves in the world and in our relationships with others. I have found that the most successful, long-term solution to anxiety involves several components, and what works best varies with each individual. Learning about your irrational thought patterns and changing them is very important; so is learning techniques to calm your inner state and change what you feel. Altering ingrained patterns of behaviour that contribute to reinforcing the anxiety helps as well. Sometimes, it is also useful to explore how and when this anxiety was developed as a reaction; it can make it much easier to let go of these patterns when we understand how and why they were developed, when and where, and in reaction to what specific experiences. Understanding their relevance in the past, makes it easier to change them in the present.