More technically, the valve, when engaged, changes the
key of a trombone from Bb to F.
Historically, a "Bass Trombone" was one that had pitch lower then a "Tenor Trombone"; valves not necessary. Contrabass Trombones with double slides were in common use up until the late 19th century, later in England, and up to today in a few brass bands. The Bb/F "Bass" Trombone was introduced in 1839. With one rotaty valve the scale of a otherwise tenor-voiced 'bone is extended down to low C, the lowest note playable on a traditional "straight' bass 'bone.
In the 20th century trombones with two valves have appeared , and of those, there are two different types. One type has dependent valves, meaning that the second valve is only useful if the first is engaged, and the other provides valves that work independently of each other. With both valves engaged the pitch is changed to either E or Eb depending on the player's choice of the tuning valve. With only the second valve engaged the pitch would be D (or Db).
Because the slide positions are determined as a fraction of the total length of the instrument (as opposed to a fixed difference between all adjacent positions), there is not enough room on the slide for all 7 positions when a valve is engaged. With a larger difference in positions, with one valve engaged there are only 6 positions, with both engaged 5.
To put this in context: The second valve on both a euphonium and a trumpet do the same relative thing - drop the pitch a semitone, but the formers is twice as long as the laters. This is because euph's tubing are twice as long as that of trumpets.
It is now quite common for players of Tenor Trombone parts to play on a Bb/F horn due to its flexibility. So all straight trombones (of the right length, there are alto and soprano trombones) are tenors and all two valve trombones are basses, single valves can be either, depending on the bore, and what the manufacture decided to call it.
All of this makes sense if you consider that back in the day of hand made instruments each region would have its own set of what constitutes a {voice} trombone. You just used the instruments that was easiest for a particular part. With only a handfull of manufactures relatively mass producing horns for the entire world things have normalized down to more clear types. This makes things infinitely easier for composers, arrangers, players, and instructors. Unfortunatly, due to this history there are some lines in some works that can not be performed on modern instruments - ie slurs that cross a harmonic. The inclusion of the second crook for the second valve elevates this somewhat by increasing the possibilities, but it would mean for a piece the player would be playing on a horn that they're not used to - most everyone plays with the Eb crook all the time unless they have a good reason not to.
See also: music terminology
Mainly from my brain, with historical dates from The New Grove Dictionary