late 14c., "urgency, insistence" (a sense now archaic), from Old French instance "effort, application; urgency, eagerness, anxiety" (13c.), from Latin instantia "presence, effort, intention; earnestness, urgency," literally "a standing near," from instans (see instant).
In logic, "a fact, a case, an example" (a sense in English from early 15c.), from Medieval Latin instantia, which translated Greek enstasis. This led to for instance "as an example" (1650s), and the noun phrase give (someone) a for instance (1953, American English). The general sense "anything that illustrates a general type" was in use by 19c.
"cite as an instance" (in the logical sense), c. 1600, from instance (n.). Middle English had a verb instauncen "to plead with, urge, entreat." Related: Instanced; instancing.