A unit of measurement of planar angles, equal to 1/90 of the right angle; denoted by ${}^\circ$. A degree is subdivided into 60 minutes ($60'$) or 3600 seconds ($3600''$). A right angle has 90 degrees, a straight angle has 180 degrees. Degrees are also used to measure circular arcs (a full circle has 360 degrees).
Due to computer necessities and increasing precision, computations are more often done in decimal parts and no longer in degrees, minutes and seconds.
Sometimes, a degree of a number $a$ is an expression of the form $a^b$ where $b$ is also a (suitable) number, see Power.
There are numerous other ways in which the word degree is used. E.g. degree of a polynomial; degree of a mapping; degree of unsolvability, degree of irrationality, and many more. It is also, of course, the name of the unit for temperature measurements in various scales.