Liquor is a synonym for alcohol, usually a fermented drink that has been distilled. Distillation is basically the process of taking a fermented liquid and purifying it which removes water and therefore makes the concentration of alcohol higher. In North America, hard liquor is a common synonym.
As a verb, to liquor something is to either coat it with oil or grease, or it can mean to drink enough alcohol to become drunk. The latter definition is usually used with the preposition up.
Liqueur is a liquor that is mixed with herbs and spices, usually to make the flavor sweeter.
There are caveats to these definitions. For example, there is a chocolate liquor and a chocolate liqueur. The liquor is a distillation of fermented cocoa beans. The liqueur is a alcoholic beverage which tastes like chocolate.