the delay usually refers to the fact that you have to move your feet from "heels on the floor" to a position on the pedals where you can apply brakes.
Often one needs to keep the aircraft straight with rudder and it takes a couple of seconds to move your feet, also, if you apply manual braking immediately on touchdown it may cause the Nose gear to slam onto the runway, whereas if you have selected "autobrake" the braking process commences faster and probably smoother.
Hope that helps.