It is one of the ways used to extend the duration of sound (a note) or silence (a rest).
Let's use an example to clear this up. A half note is 2 beats long. With a dotted half note, we'd hold the note for 2 beats, plus half of it's original value, which is 1 beat. Therefore, we hold the note for a total of 3 beats long. 2 beats (original value) + 1 beat (half of original value.)
Get it? No? Let's try again. What if we did a dotted quarter note? How long would that be held for? Well, let's follow the formula. A quarter note is 1 beat long. For a dotted quarter note, we'd play and hold the note for the original value plus half of its original value. For the dotted quarter note, you would hold it for 1 1/2 beats (the length of 1 quarter note and 1 eighth note.)
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