This algorithm is used to find the greatest common divisor (GCD) of two integers and their corresponding Bezout coefficients, which can then be used to find the modular inverse of one of the integers. Specifically, if a and m are integers with gcd(a,m)=1, then there exist integers x and y such that ax+my=1. Solving this equation for x gives the modular inverse of a mod m, which is x mod m.