A doctrine developed primarily by the Scottish philosopher David Hume (1711-1776) and the English psychologist David Hartley (1705-1757). (Psychology and philosophy of mind were not then distinguished, but Hartley offered a physiological basis for what in Hume was a purely mentalistic doctrine.)
Ideas, regarded rather as sensations or as mental images, were associated in the mind according to certain laws, mainly concerning contiguity and resemblance, and thereby led to further ideas, and to the functioning of mental life in general.
The doctrine had analogies to physical theories whereby physical atoms moved under the influence of physical laws like that of gravitation. Eventually it came to be rejected - for example, by Francis Herbert Bradley (1846-1924) and Henri L Bergson (1859-1941) - because such psychological 'atoms' are not in fact to be found and the proposed mechanism was far too simplistic; also, it was not always clear whether contiguity and resemblance apply to the ideas themselves or to the things they are of.
Associationism is also called 'association of ideas', a phrase apparently due to the English philosopher John Locke (1632-1704), in his Essay Concerning Human Understanding.
The doctrine, however, has far older roots, going back to Greek thought and even to primitive 'sympathetic' magic. An allied modern doctrine is that of the conditioned reflex.