What does a strong acid mean?

Usually an acid with a pH of about 1 or 2. Some examples are hydrochloric acid (HCl), nitric acid (HNO3) & sulfuric acid (H2SO4).

More specifically a strong acid is a substance that when dissolved in water, completely dissociates into ions with the positive ion being hydrogen (H+). This usually does yield a very low pH unless the acid itself is in a very low concentration.