An acid, HA, undergoes the following equilibrium in water:
HA(aq) + H_2O(l) rightleftharpoons H_3O^+ + A^-
For strong acids, this equilibrium lies strongly to the right; and for weak acids, the equilibrium lies to the left (as written, i.e. as we face the scree).
As for any equilibrium, we can write equality of forward and reverse rates, i.e. the condition of equilibrium, as:
K_a = ([H_3O^+][A^-])/([HA(aq)])
K_a is thus simply a number that must be measured for different acids at different temperatures; there is wide disparity in K_a values. For strong acids, K_a values are large (typically greater than 10); for weaker acids, K_a are much smaller, and the equilibrium equation lies to the left.
pK_a values, where pK_a=-log_10K_a, are another refinement to this approach. The stronger acids typically have NEGATIVE pK_a values...i.e. the extent of protonolysis is generally considered to be quantitative