The word degree has several meanings:

1. A unit for measuring temperature. When you check if you have a fever, the thermometer might read 101 degrees Fahrenheit. Water freezes at 32 degrees Fahrenheit and boils at 212 degrees. Scientists often use Celsius instead, where water freezes at 0 degrees and boils at 100 degrees.
2. A unit for measuring angles and directions. A full circle contains 360 degrees. When you make a right angle with your arms, that's 90 degrees. If you turn completely around, you've rotated 360 degrees. Navigation uses degrees too: a ship might sail on a heading of 270 degrees to go west.
3. An academic title earned by completing a course of study. After four years of college, students typically earn a bachelor's degree. Doctors, lawyers, and professors often hold advanced degrees that required additional years of study. When you graduate from high school, you receive a diploma, but graduating from college earns you a degree.
4. The extent or amount of something. If you say “I agree to some degree,” you mean you partly agree. A problem might be serious “to a high degree,” meaning it's very serious. This usage helps express how much of something exists, like saying “She succeeded to an extraordinary degree” instead of just “She really succeeded.”