Well obviously acidity is related to H+ ions floating around. Therefore, a stronger acid will have more H+'s in solution caused by more H+'s falling off.
Now picture this...
There is a steady amount of relative electron density in a molecule. Let's say, loosely and for just consistency, that the electron density is 2 (arbitrary number).
Cl- has an extreme amount of electronegativity which also means it attracts more electron density. In HCl, the CL has so much of the electron density, that the H begins to seem more and more positive. For example, if CL had 1/2 of the electron density it would get the arbitrary number 1 and H would get a 1. But if CL had a electron density of 1.5, it would feel more of the electron presence making it more negative and the .5 for the H would make it semi positive to counteract that negativity.
Therefore, the H has an easier chance of falling off when involved with an electronegative element.
However, make sure not to confuse this with why HI is stronger than HCl. That has is a different story..