The noun degree has 7 senses (first 6 from tagged texts)
1. (27) degree, grade, level -- (a position on a scale of intensity or amount or quality; "a moderate grade of intelligence"; "a high level of care is required"; "it is all a matter of degree")
2. (17) degree, level, stage, point -- (a specific identifiable position in a continuum or series or especially in a process; "a remarkable degree of frankness"; "at what stage are the social sciences?")
3. (15) academic degree, degree -- (an award conferred by a college or university signifying that the recipient has satisfactorily completed a course of study; "he earned his degree at Princeton summa cum laude")
4. (7) degree -- (a unit of temperature on a specified scale; "the game was played in spite of the 40-degree temperature")
5. (7) degree, arcdegree -- (a measure for arcs and angles; "there are 360 degrees in a circle")
6. (6) degree -- (the highest power of a term or variable)
7. degree -- (the seriousness of something (e.g., a burn or crime); "murder in the second degree"; "a second degree burn")