Tone, as guitarists and bassists refer to it, means timbre (which is confusingly pronounced "tamber" or "tambour.") It means every part of the sound of your instrument that is not the fundamental pitch. If you want to get a sense of timbre, play the A on the 12th fret of the third (A) string, then play the A on the 17th fret of the fourth (E) string. The first will sound "brighter" or "clearer" or "more articulate." The latter will sound "warmer" or "rounder" or "duller." They have the same pitch, but they do not sound the same.
Some terms you might hear attributed to a bass' tone are as follows:
Positive
Warm (opposite of bright)
Bright (opposite of warm)
Dark (also an opposite of bright, but not the same as warm)
Clear (opposite of dull or muddy)
Articulate
Jangly (most basses are not jangly, this refers more to guitars)
Growly
Burpy
Piano tone/Piano like (also referred to as "shimmering overtones")
Punchy (hard to explain, bug you'll know it when you hear it)
Upright like (sounds similar to a double bass)
Zingy
Rich (this has many meanings)
Boomy (can also be a negative)
Mwah (typically used when discussing the articulation of fretless basses, but some fretted basses can have a bit of mwah)
Wably/warbles/beating (refers to a sound artifact that occurs when two notes of similar pitch are played together. Technically this is an aspect of pitch, but it also kind of isn't pitch)
Tubby (might also be a negative)
Crisp (generally refers to the attack)
Smooth
Aggressive
Chimey (not very common in basses, more relevant to guitars)
Woody
Rumbly
Negative
Dull
Muddy
Thuddy (can also be a positive)
Farty (very rarely can be a positive)
Clanky
Clangy (sometimes can be a positive)
Boomy (can also be a positive)
Bland
Inarticulate
Inharmonicity (a kind of chorusy sound that occurs when a sting is too thick. Might be useful in some cases, but generally should be avoided. Playing higher up on the lower strings adds to this attribute)
Flabby/Flubby
Ice picky/icepick highs (more an issue with guitars, but basses can have it too. Typically remedied with amp EQ)
Most of these are kind verbal attempts at onomatopoeia, many are self explanatory, and typically you will know them when you hear them. There are many more as well.