Why does the PH lower when you dissolve an acid in water?

Very simple.

Add acid to neutral solution (i.e. water) makes it more acidic (i.e. lowers the pH) overall.

Intuitively it is similar to adding a cold solution to a warm one - the mixture's temperature will be somewhere between the two.

Technically, pH is an inverse measure of the concentration of H+ ions (ph=-log[H+]) - that is, the more H+ ions, the lower the pH. Acidic solutions have a lot of H+ ions, water doesn't; so adding some acid will increase the number of H+ ions and therefore decrease the pH.

If you add an acid to the water, you increase the concentration of hydrogen ions. pH is a measure of the hydrogen ion concentration:
 The technical explanations is:
At 25°C pure water dissociates:
 H2O ? H+ + OH-
It has been found that the molar concentration of H+ ions in pure water is 0.0000001M or 10^-7M

Now if you calculate the pH:
 pH = -log [H+]
pH = -log 10^-7
pH = 7.00

Now you add some acid to the water. The acid dissociates to produce more H+ ions
The molar concentration of H+ ions can have increased to 10^-3M ( this is a higher concentration of H+ ions compared to pure water)
Again:
 pH = -log [H+]
pH = -log 10^-3
pH = 3.00

By adding acid to the water you have increased the H+ concentration and  the pH has dropped from 7.00 to 3.00.

When dealing with pH forget about such old fashioned expressions as" the potential hydrogen ion concentration" This is only confusing. The p in pH is interpreted as " negative log of [H+]", in exactly the same way as pOH is = -log [OH-] and pKa = -log Ka, etc.