。
We couldn't play because of the rain.
Literal
We [topic-は] rain [because-of-のために] play-can-not-[past].
~のために ('because of / due to,' with a noun) is the causal sense of ために — distinct from its purpose sense ('in order to'). Context usually disambiguates: with a noun + の, it's causal; with a dictionary-form verb, it's purpose. 遊べなかった is the past negative of the potential 遊べる.