The color gray is used in World of Warcraft to indicate a lack of usefullness or benefit to the player. For example, gray items can only be sold to a vendor - they aren't good for anything else. Another example is a crafting recipe colored in gray; while what one produces from the recipe may be quite useful, producing it has no chance to raise the player's skill in that profession.
Gray items are often referred to as Vendor Trash. These are items that generally have no good use compared to other items you could get that are of higher quality.
Gray items, despite their uselessness, can sometimes sell for a good amount to a vendor.
Gray mobs are of a level much lower than yours. These mobs do not give experience. Once a mob is grey to you, it is normally quite easy to kill. There are some exceptions though.
Also, if, when the mob in question is targeted, and the plate at the top of the screen indicates its name with a yellow name on a gray background, it might be said to be gray. This means that someone else will be credited when that mob is killed.
Gray Levels (PvP)
In PvP, when someone's level is gray to you, you cannot gain any Honor points from them. So, in other words, it is not worth your time to kill them.
In your quest window, a quest shown in gray is intended to be completed at a much lower level than your current level. You will receive little, if any, experience for completing gray quests.