The remainder term, also known as error or residual term, represents how close our approximation using a truncated version of the Taylor series is to the actual value of the function. It quantifies how much we've left out by stopping at a certain number of terms in our approximation.
Related terms
Truncated Taylor Series: An approximation obtained by taking only up to a certain number (n) terms in a Taylor Series.
Order of approximation: The highest degree term included in our truncated Taylor Series; determines how many terms are used in the approximation.