Circle of 5ths

The circle of 5ths is an organizational system for key signatures. Roughly modeled after a clock, the circle indicates the 12 (15 including enharmonic keys) different key signatures for the Major and relative minor keys.
Each key signature (you can think of as a logo for tones to be used in a given piece of music) represents a Major key and a minor key. This is called relative keys. Each key signature has a minor key that is the relative of the Major key (2 keys per logo [signature]- a Major and a minor one).
Key signatures are indicated at the beginning of a piece of music (right after the clef and before the time signature).

Some Pointers about the Circle of 5ths

A key signature indicates which family of tones will be utilized for a given piece of music.
In tonal music, it is an arrangement of sharps or flats which define pitches to be used. Sharps & flats can be mixed in a key signature, but not in this basic set of Major keys.
Each key signature defines a diatonic scale in two modes: Major & minor.
The natural minor can be found by beginning the Major scale on the 6th scale degree.
A diatonic scale is one which utilizes the seven pitches defined by a key signature for melody & harmony. Diatonic means 'within the key or across the tones of a key center'.

Is the minor key signature really the same as the Major? (Are they really relatives?)

The natural minor key tones are identical to its relative Major key. They share the same tones (chords & scales), but calling a different chord the one (calling vi of the Major key the i).
Natural minor is a member (somewhat viable, but cannot fully stand on its own harmonically) of the minor key family. Yet, it truly doesn't relate (isn't a true relative harmonically) of the relative Major. For example, A minor is a modification of A Major and ultimately isn't 'born of' C Major.
The Circle of 5ths, in one view, is an incomplete organizational system for key signatures. Even with its positive aspects, it has a limiting quality that doesn't show the complete picture (the relationship between Major & minor). Plus, it can be difficult to memorize. Often, using a set of visual tools allows for quicker memorization. For memorizing how many sharps or flats are in a key, we've built the Lines of 7.
You have choices on how you view tonal music. If you choose not to learn about the 3 versions of the minor keys (natural, harmonic, melodic), that is your decision (and a common one for non-advanced students). If you decide to learn the 3 forms, you'll know a bunch of cool (and potentially limiting) stuff, depending on how you view it.
After you put in the time to learn it, keep in mind that most people will have no idea what you are talking about when you try to explain it (yet, explaining it to others can help you learn it). Caveat: if you are going to play Jazz, put in the time and learn it. You'll need to know the modes & the chords derived from the minor key system. There are a lot of useful & great sounding melodic & harmonic potential on the minor side of the street.
Someday, we might not have this conversation because there may be a more suitable minor key signature learning tool.
Chords in ALL Major Keys