Gematria /ɡəˈmeɪ.tri.ə/ originated as an Assyro-Babylonian-Greek system of alphanumeric code/cipher later adopted into Jewish culture that assigns numerical value to a word/name/phrase in the belief that words or phrases with identical numerical values bear some relation to each other or bear some relation to the number itself as it may apply to Nature, a person's age, the calendar year, or the like.
Similar systems, some of which were derived from or inspired by Hebrew gematria, have been used in other languages and cultures, i.e. Greek isopsephy and Arabic abjad numerals.
The best-known example of Hebrew gematria is the word Chai ("Alive"), which is composed of two letters that (using the assignments in the Mispar gadol table shown below) add up to 18. This has made 18 a "lucky number" among Jews, and gifts of money / donations given in multiples of 18 are very popular.
Although the term is Hebrew, it is derived from the Greek γεωμετρία geōmetriā, "geometry", which was used as a translation of gēmaṭriyā, though some scholars believe it to derive from Greek γραμματεια grammateia "knowledge of writing". It's possible that both Greek words had an influence on the formation of the Hebrew word. (Some also hold it to derive from the order of the Greek alphabet, gamma being the third letter of the Greek alphabet (gamma + tria).) The word has been extant in English since the 17th century from translations of works by Giovanni Pico della Mirandola. Although ostensibly derived from Greek, it is largely used in Jewish texts, notably in those associated with the Kabbalah.