1836, "quality of leaping;" 1849, "quality of standing out, state of projecting or being projected;" see salient (adj.) + -ence. The psychological sense of "quality of being more prominent in the mind or memory" is by 1938.
1560s, "leaping," a heraldic term, from Latin salientem (nominative saliens), present participle of salire "to leap," from a PIE root of uncertain form (source also of Sanskrit sisarsi, sisrate "to flow, run, hurry;"Greek hallesthai "to leap," Middle Irish saltraim "I trample," Middle Welsh sathar "trampling").
The meaning "pointing outward" (preserved in military usage) is from 1680s; that of "prominent, striking" first recorded 1840, from salient point (1670s), which refers to the heart of an embryo, which seems to leap, and translates Latin punctum saliens, going back to Aristotle's writings. Hence, the "starting point" of anything.