Why is my fridge light on?

Generally there is a door switch that controls whether the light is on or not, but without knowing the model number of your refrigerator we can't say exactly where that switch will be located; they're frequently found near the top of the door frame, but can be anywhere along the top, edge or bottom of the door frame.

Once you locate the door switch, you should be able to manually press it and see if the light goes off when it's pressed. If it doesn't, chances are the door switch has failed and needs to be replaced. That would be my first approach, but testing it with a multimeter will confirm whether it's working or not. It's also possible there's an issue with the wiring to the switch and/or the control system, but the switch is the first place to look at.