Resonance occurs in the conjugate base of the carboxylic acid between the C=O and the C-O-
In a resonance structure the electrons are more spread out as they cover a larger area and are not held on one atom as a lone pair are. This means the pair of electrons are less available to bond with H+ (this is what makes it 'more stable'). If it is less attractive to H+ then by definition it is a weaker base and so the corresponding acid must be a stronger acid.
Compare to alcohols which are not acidic as they do not donate their H+ in aq solution.
Unlike the carboxylate ion, the lone pair on an alkoxide ion (an alcohol which has lost its H+) is localised and held on the oxygen atom. This increases the electron density and makes it much more attractive to H+ this means the alkoxide ion is a very strong base and so the conjugate acid (alcohol) is a very weak acid (so much so it does not donate the H+ aq solution.