The degree system is used in some traditions to keep track of who has the most training, and has been doing this the longest.
Not all traditions have degrees; most of those that do, have three - I suppose because Gardner used three. (Gerald Gardner, by the way, was in many ways the Father of the modern neo-pagan religion of Wicca, whether we really like it or not. Most of the Wiccans in this country could trace their roots back to his original group, one way or another, and without them and their writings the face of Wicca in this country would likely be very different.)
Traditionally, you spend a year and a day studying before you are initiated. When you are initiated, you become a first degree witch; a Priestess or Priest. Then you study for another year and a day, and get elevated to second degree; a High Priestess or High Priest. After another year and a day you can be elevated to third degree; still High Priestess or High Priest, but you can draw a different sigil after your name, if you are so inclined.
In our tradition, we use a degree system. First degree is the dedication, when you have decided that you belong on this path, and dedicate yourself to the Lord and Lady. Second degree is earned when you begin to see the patterns unfolding in the world around you, and can predict them. Third degree is gained when you begin to use the patterns, and go out to teach and heal.
Other traditions may do it differently. If you belong to an established tradition, ask them. If you are working as a solitary, or making your own tradition, do what seems best to you. You can always change your mind later! If you aren't interested in this path at all, but were just curious, this is one answer.
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