It's a common acronym for “electric upright bass.” Mikael Jansson describes such basses as follows:
An EUB is a double bass intended for being played electronically amplified. Most EUBs are solid, a few have hollow bodies, although smaller in size than regular acoustic double basses.
For all other purposes, EUBs are played using the same technique as on an acoustic double bass (plucking, bowing, slapping).
The difference between an EUB and an electric bass guitars is that the fingerboard is arched and fretless (although fretted EUBs exist), and the bridge is usually made of wood (other materials—metal, graphite—have been used, however rarely).
Then there are hybrid instruments: EUBs that can also be strapped on and played like bass guitars, fretted EUBs, EUBs that have shorter scale than regular double basses, and EUBs that have pickups that can generate MIDI signal, for driving synthesizers and similar devices.
Most EUBs have a scale length similar to the double bass, i.e. ca 42 inches. A number of EUBs, however, have scale lengths between 34 and 36 inches, like bass guitars or a 1/4 size double bass. A few EUBs have even shorter scales, and some players/makers have even converted electric cellos into EUBs by using thicker strings.
Some EUBs have detachable necks, for logistical purposes. In the beginning, EUBs were mostly built as a more portable alternative and louder to the acoustic double bass, the string bass could at last compete with drums and electric guitars in popular music. A few players have however taken advantage of the sonic possibilities the EUB offers (David Friesen[1], Eberhard Weber[2], etc).
Most EUBs have some kind of piezo transducer pickup system, however quite a few also have a magnetic pickup system in combination with the piezo. Many use off-the-shelf systems such as Underwood[3], K+K[4] or Fishman[5], although a number of makers have designed their own systems.
EUBs often have an endpin similar to an acoustic bass. It is however quite common to see EUBs standing on a tripod stand.
An EUB is an instrument in its own right, in some aspects similar to the acoustic double bass, in other aspects different. Just like a Stratocaster guitar differs from a Spanish guitar.

