Well it depends on which elasticity we are looking at. If we are considering the price elasticity of demand, shown right, then having an elasticity measure of -.2 means that as price goes up by some percent change, then quantity goes down by that percent change multiplied by -.2.
This is a good result, because it is saying that as the price goes up, we demand less of that good. How much less of the good, only -.2, which means that the good is INELASTIC. As long as the elasticity measure is below 1 (or above -1), then the quantity changes at a relatively lower amount than price, so we call that inelastic. See the post on elasticities for more of an explanation.
What if the price elasticity of supply was -.2? Then we would be saying if price
went up, we would supply less, and that doesn't make sense.
What about cross price elasticity of demand? With a negative elasticity, it means that the goods are complements. Why? Because if the price of hot dog buns goes up, we demand less hot dogs (they are complements, so making buns more expensive also lowers demand for the dogs). If the elasticity measure was positive, then the goods would be substitutes. If the price of pepsi goes up, we demand more coke (both are positive so we get a net positive). Make sense?
Finally, the income elasticity of demand. If we get an elasticity measure of -.2 then that means that as our income goes up, we demand less of the good. This would be an inferior good, like top Ramen, or perhaps ground beef. PBR may be another good example.