In early times, salt was substantially more significant than it is today. (E.g., see the etymology for salarium at Wikipedia.)
Salt has some association with holiness; it was part of the grain offerings (Leviticus 2:13 [NIV]):
Season all your grain offerings with salt. Do not leave the salt of the covenant of your God out of your grain offerings, add salt to all your offerings.
This contrasts with verse 11 (NIV) prohibiting the inclusion of yeast:
'Every grain offering you bring to the LORD must be made without yeast, for you are not to burn any yeast or honey in an offering made to the LORD by fire.
In 1 Corinthians 5:8, Paul associates yeast with "malice and wickedness" (NIV).
Salt is also important as a preservative and a seasoning. This points to the fact that Christians are supposed to be positively effective in the world.
Perhaps most significantly salt is similar to light (another image Jesus used) in being beneficial, distinctive (salty is a major aspect of the sense of taste, light defines the sense of sight), powerful (a little salt or light goes a long way), present in the world (salt was part of everyday life, a light is not hidden under a basket), and even a bit disruptive or annoying (e.g., early morning light can be annoying when one is tired, salt can be similarly unpleasant) while also being attractive (one tends to be drawn to eating salty foods not unlike how one tends to be drawn to a lighted area).