late Old English, the second book of the Old Testament, from Latin exodus, from Greek exodos "a military expedition; a solemn procession; departure; death," literally "a going out," from ex "out" (see ex-) + hodos "a way, path, road; a ride, journey, march," figuratively "way out, means," a word of uncertain origin. The book is so called because it tells of the departure of the Israelites from Egypt under the leadership of Moses. General sense (with lower-case -e-) "departure from a place," especially "the migration of large bodies of people or animals from one country or region to another," is from 1620s.
Beekes derives the Greek word from PIE *sod- "course" and says it is traditionally connected with Slavic words for "course" (such as Russian xod "course, progress," "which might have been borrowed from Iranian") and adds that it is perhaps also related to Sanskrit a-sad- "to tread on, go on," Avestan apa-had- "to go away; become weak," "but the relation between them is unclear, as is the connection to the PIE root *sed- "sit" (proposed in Watkins, etc.)."