Synthetic division is a method for dividing polynomials using successive multiplication and subtraction steps. It involves writing the coefficients of the terms, drawing a box around the number being divided by with a line below, then bringing down the first term and repeatedly multiplying and adding until reaching a remainder. For example, to divide (2x-7) by (x=3), write the coefficients 2 and 7, box the 3 with a line below, bring down the 3, and repeatedly multiply and subtract until getting a final remainder.