You're spot on. This painting is indeed based on the legend of Zeus "coming" as a shower of gold. :) The woman he impregnated was called "Danae" and their child was the hero Perseus.
Klimt's painting is beautiful. I especially love the gold leaf which is so perfect for the subject. Though I think my favorite painting depicting Danae and Zeus coming as a golden shower would be Correggio's which is also on this site.