c. 1300, skippen, "spring lightly; go with a leap or bound; take light, dancing steps," also "jump over," probably from a Scandinavian source such as Old Norse skopa "to take a run," from Proto-Germanic *skupan (source also of Old Swedish skuppa, dialectal Swedish skimpa, skopa "to skip, leap"). Related: Skipped; skipping.
The meaning "omit intervening parts (in reading or narrating), read over" is recorded from late 14c. Command skip it "drop the topic, leave off talking about it" is by 1934.
The meaning "to bounce" is from mid-15c.; the sense of "cause to skip or bound," especially of a thrown thing, as a flat stone across water, etc. is from 1680s.
It is attested by mid-14c. as "to run, go, rush, flee," also "to make off, hasten away. To skip out "run out, flee" is by late 14c. (in Middle English it also meant "leap up, spring forth"). The modern transitive meaning "fail to attend" is attested by 1905, perhaps ultimately from skip school (attested by 1810).
The custom of skipping rope, "jumping a rope slackly held at both ends and in steady motion over one's head" has been traced to 17c.; it was commonly done by boys as well as girls but by late 19c. was described as "a common amusement of young girls." [Century Dictionary, 1895]