Do you understand how a bimetallic strip in a thermometer works?
You have two dissimilar metals like copper and steel which expand and contract from heat at different rates. As the strip or coil of metal heats and cools, the expansion of the two metals causes it to curl in proportion to the temperature. That, in turn, moves a pointer or activates a switch, etc.
The same things happens with film and photographic paper. You have two materials which react to moisture in different ways. The emulsion absorbs a lot of water but the base absorbs very little. As the two layers expand and contract in proportion to their moisture content, they will cause the film to curl. This is what causes the effect you are seeing.
If you like to experiment, you can use a piece of film or photographic paper as a hygrometer. Tack a piece of film or paper to the wall by one corner then watch its response to the humidity in the air.
I actually have a piece of photo paper tacked to my darkroom wall which I use as a makeshift humidity indicator. I know just how much it should curl when the humidity is right. If it curls too much or too little, I know that I have to turn my dehumidifier on or off, depending on how the paper reacts.
This effect can also be a good indicator of when your film is dry enough to handle. Just watch the curl and, when it flattens out, your film should be almost dry.