As a musician, understanding music theory is very important as it is the foundation behind all music. Music theory aides one in sight-reading, memorization, improvisation, song writing, and just about any other musical skill. However, for the musician who is self-taught, it may be difficult to start learning simply because there is so much information out there! I can tell you that the Circle of Fifths is one of the best places to start.
The circle of fifths is an easy to understand diagram telling you how many sharps or flats are in each key or scale. We'll start with the keys outside of the circle, which are the "Major" keys. The top key "C" has no flats and no sharps. If you move to the right of the circle, every key past "C" gains 1 sharp. For example, "G" contains one sharp, "D" contains two sharps, and so on. For 99.99% of music, you will only need to the sharp keys up to "C#" (which contains 7 sharps).
If you move to the left of the circle, every key past "C" gains 1 flat. For example, "F" contains 1 flat, "Bb" contains 2 flats, and so on. For just about all music, you'll only to know your flat keys up until "Cb" (which contains 7 flats).
The notes on the inside of the circle works the same way, however, it is instead dealing with flats or sharps in the "Minor" keys. "a" has no sharps or flats, and every key to the right of "a" gains 1 sharp, and every key to the left of "a" gains 1 flat.
If a major and minor key both contain the same number of sharps or flats (they're similar in position on the circle of fifths), then this means that they are considered relative. For example, the minor key "a" is the "Relative Major" of "C", and the major key of "C" is the "Relative Major" of "a".
Why is it called the Circle of Fifths?
Why is it called the Circle of Fifths? This is because every pitch is a fifth away from the previous. For example, from "C" to "G" is a fifth up, and "G" to "D" is a another fifth up, and so on. This works similarly for the flat keys except that you are moving in fifths downward. From "C" to "F" is a fifth down, and "F" to "Bb" is another fifth down, and so on.
How is this useful?
Learning the circle of fifths is useful because once you memorize and become familiar with all the sharps or flats in all the common keys (up to 7 sharps or flats), then you can begin learning your scales (if you haven't already began), which is perhaps the most fundamental and important piece of music theory.
It's also important to note, that the circle of fifths is only a tool to get you started in the memorization process, once you memorize all the sharps or flats in any given key, it's important to break away from it so you no longer rely on it. You want to get to a point as a musician where you know your keys like it's the back of your had. Just remember that by learning and memorizing this well, you are setting a great foundation in your knowledge of music theory!