I dunno if it’s the case in the US, but here in BC I’ve always been told April Showers bring May Flowers, cos there’re days that it’s nice enough and you think it’s spring but then it’s raining cats and dogs the next day, so.
This one I’ve heard before — I always interpreted it to just mean April tends to be rainy, though. (And… that the rain is good for the things that grow in May? And maybe something about Pilgrims? I don’t really know.)