These are weak acids with a carbonyl group and an alcohol group attached to the same carbon.
Carboxylic acids react as most other acids do, apart from their reactions are often slower. This means when they are dissolved in water they dissociate like other acids.as shown in the euation below.

The dissociation of Carboxylic Acids
The difference in the reactions between carboxylic acids and stronger acids, e.g. HCl, can be shown in a few simple tests
Acid + Magnesium
2HCl + Mg → H2 + MgCl2
This is a vigorous reaction with lots of colourless gass given off during effervesence.
2CH3COOH + Mg → H2 + (CH3COO)2Mg
This reaction is slower and although there is still effervesence, it is not as vigorous.
Acid + Sodium Hydrogen Carbonate
HCl + NaHCO3 → NaCl + H2O + CO2
This is a vigorous reaction that is over very quickly
CH3COOH + NaHCO3 → CH3COONa + H2O + CO2
This takes longer to complete but there is still some effervesence.
NaHCO3 is used as a test for carboxylic acids
pH test
Using full range indicator, the carboxylic acid goes orange, and the hydrochloric acid turns red. When a pH meter is used, the carboxylic acid gives a reading of about 2 whereas the hydrochloric acid gives a reading of 0.5
The weak acidity is all due to the extra stability the ion has. This is because of resonance. The two oxygen atoms, being so close together on the molecule are able to share out the charge between them. When a charge is spread out over a larger area, it becomes more stable. The resonance structures of the ethanoate ion are shown below

The Resonance Structures of the Ethanoate ion
The carboxylate group is also important in that it can form Hydrogen Bonds. This is because there is a Hydrogen attached to a very electronegative oxygen atom, so it can bond with other electronegative Nitrogen, Oxygen or Fluorine atoms. The carbonyl oxygen is also very electronegative so can also take part in hydrogen bonding. This leads to the formation of Carboxylic acid dimers, as shown below:

Ethanoic Acid dimer with hydrogen bonding
This type of bonding is also important in proteins, as it is hydrogen bonding btween the NH group on one amino acid and the C=O on another amino acid that helps hold the protein together.