It's actually, as you might expect, a slightly corrupted nautical term.

On a sailing vessel with more than three masts, the aft-most and shortest mast was often referred to as the "jigger-mast" or sometime just contracted to "jig".

Because this mast was shorter hands assigned to work the smaller sails and less complex rigging were regarded as having a comparatively easy time of it, and were sarcastically described as jolly "jiggards" or "jiggarts" - which over time evolved into "Jack Tars"