The fretless bass is a bass guitar without frets. It operates in the same manner as most other stringed instruments and traditional guitars, but does not have any frets to act as the lower end point (node) of the vibrating string.
The way your fingertip pinches the string against the fretboard dampens the highest overtones without disturbing the middle ones, so you get a “warm” sound that is not “dull”. Dan Lasley's column Tone Loco discusses this in more detail.
Typically one plays fretless when they want a specific tone, or want to slide. If you have a good ear then you might find the fretless more fun. If you play jazz or folk/rock, fretless is fine. If you're a heavy hitting rock and roller, get frets. Just as the advanced guitarist may own a Strat and a Les Paul, the advanced bassist may own both types of basses.