Question

why it is difficult to apply brakes on a rainy day

Answer 1

It's quite simple. On a usual dry road, we can drive our vehicle normally because of the friction between the road and the tyres of the vehicle. 
But on a rainy day It's different. we find a  thin layer of water on the road on the rainy days because of the rain. This layer of water decreases the friction between the tyre and the road. And that's why when the brakes are applied in such condition, the vehicles doesn't stop so easily as usual. 
That's because of the low friction .

That's like landing a plane on the polar area of earth where we have the breaks but those breaks doesn't work easily due to the low friction between the tires of plane and the ice. Hope it helped. ^_^