c. 1300, dauncen, "move the body or feet rhythmically to music," from Old French dancier (12c., Modern French danser), which is of unknown origin, perhaps from Low Frankish *dintjan and akin to Old Frisian dintje "tremble, quiver." Through French influence in arts and society, it has become the primary word for this activity from Spain to Russia (Italian danzare, Spanish danzar, Romanian dansa, Swedish dansa, German tanzen).
In part the loanword from French is used mainly with reference to fashionable dancing while the older native word persists in use with reference to folk-dancing, as definitively Russ. pljasat' vs. tancovat' [Carl Darling Buck, "A Dictionary of Selected Synonyms in the Principal Indo-European Languages," 1949].
In English it replaced Old English sealtian, itself a borrowing from Latin saltare "to dance," frequentative of salire "to leap" (see salient (adj.); "dance" words frequently are derived from words meaning "jump, leap"). Native words used for the activity in Old English included tumbian (see tumble (v.)), hoppian(see hop (v.1)). Related: Danced; dancing.
Meaning "to leap or spring with regular or irregular steps as an expression of some emotion" is from late 14c. Of inanimate things, "move nimbly or quickly with irregular motion," 1560s. Transitive sense of "give a dancing motion to" is from c. 1500. To dance attendance "strive to please and gain favor by obsequiousness" is from late 15c.