How does Miller capacitor offers compensation? Does it slow down the circuit?

You put a capacitor from gate to the drain as feedback, so the capacitor seen from the gate is big as a result of multiplication of close loop gain and the initial capacitor .

so, how does it offer compensation by having a larger result capacitance? Large capacitance means slowing down the circuit which is not good.

In an op amp you need to provide compensation so the amp is stable with a closed loop resistive negative feedback.
This is commonly done by add a dominant 1-pole capacitive rolloff (6-dB/octave) starting at a low frequency using a miller capacitor internally so that there is good phase margin as the open-loop gain goes to 1.
The multiplication of the capacitance by the miller stage means the on-chip capacitor can be small.

Yes, it slows down that circuit but that's necessary to make it stable.
For example, comparators are similar to op amps but have no internal compensation, so they are generally much faster than op amps, but are unstable (will oscillate) in a closed negative feedback loop without a lot of added external compensation.