One of the breakers in the breaker box turns red when I switch it on. Some of my bathroom outlets do not work. This breaker is currently off, but when I turn it on, it shows a red light. What does that mean?
It's almost certainly the case that this is a GFCI (Ground Fault) breaker, or an AFCI (Arc Fault) breaker.
It is tripping because it is detecting a fault in the circuit which it is designed to protect.
The most likely cause of a Ground Fault is that you plugged in an appliance that internally has a ground fault. Unplug it. Plug it into some other GFCI protected socket in your house, e.g. a kitchen receptacle. If it trips that one too, then it needs repair. Otherwise it may be a bad GFCI.
The second most likely cause of a GFCI trip is some wiring is getting wet. The third most likely is you modified the wiring and did it wrong. GFCIs are really good at enforcing the Electrical Code.
If it's an AFCI trip, then it might be an appliance (electric blankets were basically the reason AFCIs were invented). However AFCIs were found to be fantastic for detecting wiring faults inside the walls - these are nearly always at a receptacle, switch or lamp. You may have to open up each of the outlets that has gone dead, and double check their connections. The less likely reason is a problem with the wires in the walls, but that is only likely if you recently drove nails or screws into your walls.
Depending on the breaker, it might simply be an alert light. I installed an AFCI breaker not long ago, and found that the light would indicate the reason it tripped after you reset it. There was a method to reset the light involving a button on the breaker.
If you can, try to find the model number of the breaker. You can then find a manual online, which will explain all the status light codes and how to reset the breaker