Old English eall "every, entire, the whole quantity of" (adj.), "fully, wholly, entirely" (adv.), from Proto-Germanic *alnaz (source also of Old Frisian, Old High German al; German all, alle; Old Norse allr; Gothic alls), with no certain connection outside Germanic. As a noun, in Old English, "all that is, everything."
Combinations with all meaning "wholly, without limit" were common in Old English (such as eall-halig "all-holy," eall-mihtig "all-mighty") and the habit has continued. Middle English had al-wher "wherever; whenever" (early 14c.); al-soon "as soon as possible," al-what (c. 1300) "all sorts of things, whatever."
Of the common modern phrases with it, at all "in any way" is from mid-14c., and all "and everything (else)" is from 1530s, all but "everything short of" is from 1590s. First record of all out "to one's full powers" is by 1880. All clear as a signal of "no danger" is recorded from 1902. All right, indicative of assent or approval, is attested by 1837; the meaning "satisfactory, acceptable" is by 1939, from the notion of "turning out well."
The use of a, a' as an abbreviation of all (as in Burns' "A Man's a Man for A' that") is a modern Scottishism but has history in English to 13c.