Hi Yo Gabba Gabba!
I have a three-year-old in da house....
Anyway, the multi-cache is a TYPE of cache! Other types are the traditional (single), mystery, earth cache, event cache etc. After you find all the waypoints that make up a multi-cache and you reach the final coordinates and make the final find, that's when you can log it as a find. (You'll see the multi-cache symbol as two boxes, whereas the cache symbol is one box.)
A series of caches are several traditional caches. Such as, I don't know, uh the "Twinkie" series. There may be 5 different caches in the Twinkie series and each would be a find that you'd log when you found them. To finish the series you'd simply have to find all 5.
Does that make sense?