pH is a measure of acidity or basisity (alkalinity) of a solution. It is approximately equivalent to the negative log of the concentration of hydronium (H3O+) ions. Because of the negative log relationship, increased hydronium ions translates to decreased pH.
When added to water, an acid releases hydrogen ions. Hydrogen ions in water combine with the water molecules to form hydronium ions, thereby decreasing the pH and increasing the acidity of water.
Water exposed to air is mildly acidic because it absorbs small quantities of CO2 from the atmosphere. The CO2 breaks down to carbonic acid that then dissociates to release hydrogen ions into the water, decreasing the pH.
To answer your question, acid added to water increases the hydrogen ion concentration (H+), decreases the pH, and increases the acidity.