How does a carboxyl group give a molecule acidic properties?

A carboxyl group imparts acidic properties to a molecule because it can readily donate a hydrogen ion ($H^{+}$), also known as a proton, to a base. This functional group is formed by the conjunction of a carbonyl group and a hydroxyl group.123

When a carboxylic acid loses its proton, it forms a negatively charged carboxylate ion. This ion is significantly stabilized by resonance, a phenomenon where the negative charge is delocalized—or spread—across the oxygen atoms of the carboxylate group. Because this resulting ion is highly stable, the parent molecule is much more inclined to release its proton compared to other organic compounds like alcohols, which lack this resonance stabilization.1

The overall acidity of the molecule can be further influenced by the presence of other groups attached to the carbon atom; for instance, electron-withdrawing groups increase acidity by further stabilizing the carboxylate ion, while electron-donating groups tend to decrease it.1