The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them which is equal to that prime. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.
The sieve of Eratosthenes is one of the most efficient ways to find all of the smaller primes (below 10 million or so). It is named after Eratosthenes of Cyrene, a Greek mathematician; although none of his works have survived, the sieve was described and attributed to Eratosthenes in the Introduction to Arithmetic by Nicomachus.
The sieve may be used to find primes in arithmetic progressions.
This is from Calculus Humor's wiki at http://calculushumor.wikia.com/wiki/Sieve_of_Eratosthenes!