Isopsephia is the Greek word applied to the practice of adding up the number values of words to come to a singular number usually for the purpose of making mystical relevancies or connections between otherwise unconnected words. This was made possible by the dual use of letters of the Greek alphabet to also represent numbers.
The Jewish people called it gematria, and the Muslim people called it khisab al jumal.

The most well known example of isopsephia is that of Suetonius relating the name of Nero, in Greek, to the words Idian Metera apekteine - 'He killed his own mother' - since the two have the same value according to the Greek number system:

ΝΕΡΩΝ
50+5+100+800+50
1005

ΙΔΙΑΝ ΜΗΤΕΡΑ ΑΠΕΚΤΕΙΝΕ
(10+4+10+1+50) + (40+8+300+5+100+1) + (1+80+5+20+300+5+10+50+5)
1005

Certain Greek poets used isopsephia in poetry, creating distichs and epigrams that were also isopsephs. A distich is an isopseph if the numerical value of the first verse is equal to that of the second. An epigram is an isopseph if all of its distichs are isopsephs with the same value.

Isopsephia gave rise to the practice of arithmomancy and even the Christian church dabbled in isopsephia for some time - although, more commonly using the Hebrew number system.
One example comes from the New Testament, when Jesus declares that he is "the alpha and the omega" - the beginning and the end of the Greek alphabet - and identifies himself with the 'Holy Ghost' and therefore, according to Christian doctrine, with God Himself. According to Matthew III:16, the Holy Ghost appeared to Jesus at the moment of his birth in the form of a dove; the Greek word for dove being Peristera - and the following calculation is taken as mystical affirmation of the Christian doctrine of the Trinity.

ΑΩ
1+800
801

ΠΕΡΙΣΤΕΡΑ
80+5+100+10+200+300+5+100+1
801

Isopsephia is derived from the words Iso meaning 'equal' and psephos meaning 'pebble'. The latter comes from the relatively common practice of calculating using pebbles or stones as visual aids.

~this information is a summary of the information presented in The Universal History of Numbers by Georges Ifrah on the subject.