Why should you avoid heavy braking on a wet road?
Braking dynamics in wet weather
When you are driving on wet surfaces you have less grip overall. As you brake, most of the weight of the vehicle is transferred to the front tyres. If the front tyres also have to steer, then there's less grip available for braking as some of the momentum has to be converted into another direction.
If you have anti-lock brakes then you can apply maximum braking power and the wheels won't lock, but this doesn't mean that you can go around corners any faster as there will still be a limited amount of friction.
The water acts as a lubricant on the road. If there is standing water then the tyres can ride up on top of it if the tread depth isn't sufficient to disperse the water.
The wet weather should not affect the performance of the brake callipers on your brake discs unless you have been through very deep puddles.
Motorcyclists should be especially careful of manhole covers and painted road markings as they will be more slippery. Any oil or diesel on the road will reduce the grip, too. This article has more about motorcycle braking.
Braking in a straight line
Your maximum braking power is available in a straight line because the front wheels don't have to change the direction of the car or motorbike.
If you are braking and one of your wheels hits deeper water this will cause a car or truck to pull in that direction because of the increased resistance.
Braking around a corner
If you are braking in a straight line and then start to corner you are at more risk of locking up the wheels which will cause you to travel straight on and you'll end up off the road.