The Fender Jazz bass, also called the" J-bass," came on the market in 1960. It differs from its older sister, the Fender Precision bass (to which it is ceaselessly and favorably compared, in this review and elsewhere), in that it has a thinner, rounder neck, a more asymmetrical body, and two single coil pickups instead of one split single coil. The J-bass, for whatever reason, is not imitated nearly as often as the P-bass by low end manufacturers, although higher end luthiers (the guys who make guitars) who build custom basses sometimes copy its "waist contour" body style.
The Jazz bass has a greater range of tonal variation than the Precision due to the two single coils. The neck pickup has a warm, soft-edged, woody whump, whump sound, while the bridge pickup has a bright, nasal, throaty honk (the Precision bass is nasal too, but it sounds kind of like beyrm, beyrm, while the J-Bass goes glonk, glonk, glonk). When both of its pickups are turned up, the J-bass produces a scooped mid tone that is excellent for slapping (the P-bass makes an unattractive "farty" sound when slapped due to a mid frequency spike), and this also has a hum-cancelling effect. I would call the Jazz bass more of a bass player's bass: it's more reliable, more versatile (despite its name, it's great for rock, metal, and funk as well as jazz), sexier, and it stands out better in the mix. Basically, it has more balls.
Many famous bass players own and play Jazz basses, but the only rock musicians I can think of that play them consistently are Geddy Lee of Rush and Tim Commerford of Rage Against the Machine. So here are two videos in which the Jazz bass is particularly audible, Rush's "Stick It Out" and "Bulls On Parade" by RATM. Give 'em a listen and see if you can hear the glonk.