The degree of a polynomial is the highest power of the variable in the polynomial expression. For example, in the polynomial 3x^4 + 2x^3 - x + 5, the degree is 4 because the term with the highest exponent is 3x^4. The degree helps determine the polynomial's behavior and the number of roots it can have. Polynomials can have different degrees, such as linear (degree 1), quadratic (degree 2), cubic (degree 3), and so on. The degree also influences the shape of the graph of the polynomial function. Understanding the degree is essential in fields like algebra and calculus.