If something is desirable it is worthy, so many people might want it. If you're hoping for one of the most desirable roles in a play, you have to have an excellent audition.
Popular. Attractive. In demand. Sought-after. All of these describe things that are desirable. After all, it has at its base the word desire, which describes wanting. The root of desirable is the Latin word desiderare, which means "long for, wish for, demand, or expect." It may have originated from the phrase de sidere, "from the stars."