mid-15c., "pertaining to numbers below ten;" 1650s, "pertaining to fingers," from Latin digitalis, from digitus "finger or toe" (see digit). The numerical sense is because numerals under 10 were counted on fingers. Meaning "using numerical digits" is from 1938, especially of computers which run on data in the form of digits (opposed to analogue) after c. 1945. In reference to recording or broadcasting, from 1960.
word-forming element used to make verbs, Middle English -isen, from Old French -iser/-izer, from Late Latin -izare, from Greek -izein, a verb-forming element denoting the doing of the noun or adjective to which it is attached.
The variation of -ize and -ise began in Old French and Middle English, perhaps aided by a few words (such as surprise, see below) where the ending is French or Latin, not Greek. With the classical revival, English partially reverted to the correct Greek -z- spelling from late 16c. But the 1694 edition of the authoritative French Academy dictionary standardized the spellings as -s-, which influenced English.
In Britain, despite the opposition to it (at least formerly) of OED, Encyclopaedia Britannica, the Times of London, and Fowler, -ise remains dominant. Fowler thinks this is to avoid the difficulty of remembering the short list of common words not from Greek which must be spelled with an -s- (such as advertise, devise, surprise). American English has always favored -ize. The spelling variation involves about 200 English verbs.