The term CHEER ON can be broken down into three crossword solutions: URGE (4 letters), ROOT (4 letters), and ROOTFOR (7 letters). URGE means to strongly encourage someone to do something, while ROOT is a verb meaning to support or encourage someone. ROOTFOR is a combination of the words ROOT and for, and it means to actively support someone or something. All three terms are related to the idea of cheering someone on, which is to show enthusiasm and support for someone or something.