How does rain affect wireless network data transfer?

Anything encountered between a wireless transmitter and receiver can reduce signal strength through attenuation. This not only includes solid objects like walls and doors, but "liquid objects" like rain and mist.

According to the CWNA Study Guide, 2.4 GHz signals may be attenuated by up to 0.05 dB/km by torrential rain or 0.02 dB/km by thick fog. 5 GHz signals may be attenuated by up to 0.5 dB/km by torrential rain or 0.07 dB/km by thick fog. Rain can also reduce signal strength through water accumulation on other objects (trees, leaves, absorbent walls) which serves to increase their attenuation.

Another (potentially much larger) impact of rain/fog is the adverse effect of moisture on cables and connectors not sufficiently protected against exposure.

Note that this answer assumes that you're talking about wireless transfer between outdoor devices, where the rain actually falls in between transmitter and receiver. Indoor signal strength may not be noticeably affected by rain outside.