This is the 9794th most frequent Japanese word.
被る
"被る" means "to wear (on the head)," "to cover," "to be subjected to," or "to take on (a burden or blame)."
In this sentence, '被る' means to put on or wear something on one's head, such as a hat.
帽子を被る。
To wear a hat.
Here, '被る' is used metaphorically to mean shouldering or taking on something, like responsibility.
責任を被る。
To take responsibility.
In this context, '被る' conveys the concept of being subjected to something, in this case, the rain.