With reference to WWII, what do the terms "European Theater" and "Pacific Theater" mean?
These refer to the two main areas in which the war (from the point of view of the United States) was fought.
The US was involved in WWII in two main areas. One was the area that was designated as "Europe" but which also included Northern Africa. There, the US was mainly fighting against Germany, though there were other Axis countries involved. Of course, Great Britain and the Soviet Union were heavily involved in the war in this theater as well. The second was the Pacific Ocean. There, the US (more or less on its own) was fighting against Japan.
The Allies won the war on both fronts, defeating Germany in May of 1945 and Japan in August of that same year.