Old English dyppan "to plunge or immerse temporarily in water, to baptize by immersion," from Proto-Germanic *daupejanan (source also of Old Norse deypa "to dip," Danish døbe "to baptize," Old Frisian depa, Dutch dopen, German taufen, Gothic daupjan "to baptize"), related to Old English diepan "immerse, dip," and probably a causative of Proto-Germanic *deup- "deep" (see deep (adj.)).
Intransitive sense of "plunge into water or other liquid" and transferred sense "to sink or drop down a short way" are from late 14c. From c. 1600 as "to raise or take up by a dipping action;" from 1660s as "to incline downward;" from 1776 as "to lower and raise (a flag, etc.) as if by immersing."
1590s, "act of dipping," from dip (v.). Sense of "a downward slope" is by 1708. Meaning "liquid into which something is to be dipped" is attested by 1825, in 19c. especially "sweet sauce for pudding, etc.," also "juices and fat left after cooking meat." The sense "thick, savory sauce for dunking pieces of raw vegetables" (by 1962) is probably a modern re-coinage.