After bloody Tarawa (Betio) on Kiribati (now), (The Gilberts then) the Americans were heading towards the outer rim of the Japanese protective sphere of their home island. Saipan was attacked this day in 1944 with enormous loss of life. The Western Pacific theatre went through to 2nd of September 1945. This link has some good reading. http://www.army.mil/cmh-pg/brochures/westpac/westpac.htm
Outside of the guys who fought there, nobody remembers it, because it was yet another island invasion in a war of island invasions, and two weeks after the invasion of Normandy. The "Great Marianas Turkey Shoot" is remembered, though. The Battle of the Philippine Sea.
