Something savory is full of flavor, delicious and tasty — usually something that someone has cooked. In the world of cuisine, savory is also often used to mean the opposite of sweet, or salty.
The easiest way to remember savory is that it rhymes with flavory — which is not a real word, but should be. Interestingly, the word unsavory — which is clearly the opposite of savory — is almost never used to describe food. If some a dish doesn't taste good, it, well, isn't good-tasting. If something is unsavory, then it's probably a person or situation that seems morally questionable. So, save savory for delicious food and save unsavory for things, people and ideas deserving of the adjective.