Numerology is the philosophy of attributing meaning to relationships between numbers and the real world.
In one direction, real world objects already have numbers associated with them. The coincidence of these numbers is given special significance. For example: the twelve Apostles and the Twelve Tribes of Israel. Another example: the five fingers on a human hand and the five rays of a starfish.
In the reverse direction, real world objects are assigned numerical values. Meaning is attributed to objects with the same value. For example, letters in an alphabet are given numerical values and then words with the same sum of values have a special connection. Numerical evaluation of words is the basis of the Kabbalah study of the Bible. Another Biblical example is the assignment of 666 as the Number of the Beast; natural occurences of this number are viewed as boding an evil influence.
Numerology should not be confused with superstitious attributions of meaning to numbers. For example, the superstitious belief that 13 is unlucky has little basis in the real world.