The wave function collapse and "spooky action at distance" for entangled particles are somewhat different concepts. The collapse idea arises as a part of Copenhagen interpretation, which states that particle always exists in a superposition state (aka wave function of probabilities). So when audience asks, "well why is it that my measurement device showing particle exists/doesn't exist in one place"? The interpretation then says, "That, my dear fried, is because the wave function collapsed to a single state just when you did the measurement". People have been trying to explain and figure out what/why/when this collapse occurs to make sense of Copenhagen interpretation.