If we add a dot to a note its duration will increase by half its own value:

Without Dot With Dot
Note Equivalence Note Equivalence

A comment by Gary Corcoran: A dotted note equals 3 notes of the next shorter value.

By adding an extra dot you can add half the value of the value added by the first dot. For example, if you add a double dot to a quarter note you will add an eighth (half the value of the quarter note) and a sixteenth note (half the value of the eighth note):

Double dot

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José Rodríguez Alvira.