There is no escape...believe it or not. Mathematics is everywhere.
For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term. The degree of the polynomial is again the maximum of the degrees of all terms in the polynomial.
For example, the polynomial x2y2 + 3x3 + 4y has degree 4, the same degree as the term x2y2.