This expression just means that it rains a lot in the spring. :)

The above answers are very misleading. The expression "It's raining cats and dogs" means that the rain is very heavy (as opposed to light rain like drizzle). The intensity of the rain is very high. It has nothing to do with the frequency (how often) it rains. For example if it rains every day during spring you can say "It rained a lot during spring". You cannot say "It rained cats and dogs during Spring". On the other hand if it is raining very heavily (even for 5 minutes) you can say "It's raining cats and dogs" but you cannot say "It's raining a lot". So "they say it rains cats and dogs in the spring" means during spring, when it rains, the rainfall is very heavy. It does not mean it rains often during spring.

"Raining cats and dogs" is an idiom, it means it's raining a lot. ("What does "it rains cats and dogs in the spring" mean?")

It rains a lot in the spring