"nth-degree" refers to the highest power of x in a given expression or equation. In relation to Taylor polynomials, it represents how many terms are included in the approximation.
Related terms
Degree: In general mathematics, degree indicates either angles or powers (exponents).
Coefficient: Coefficient refers to numbers multiplied by variables in algebraic expressions.
Polynomial: A polynomial is an expression with one or more terms consisting only of variables and coefficients combined through addition/subtraction/multiplication.