The functional group characteristic of carboxylic acids is known as the carboxyl group, which is represented as $-COOH$.

Carboxylic acids are a class of organic compounds that contain this carboxyl group. The structure of the carboxyl group consists of a carbon atom that is double-bonded to an oxygen atom and also bonded to a hydroxyl group ($-OH$), leading to the notation $-COOH$. Additionally, the carbon atom can be attached to either a hydrogen atom or a carbon chain. This distinct structural arrangement imparts specific properties to carboxylic acids.

The carboxyl group exhibits polarity due to the presence of electronegative oxygen atoms. This polarity enables carboxylic acids to engage in hydrogen bonding with other molecules, which generally enhances their solubility in water compared to hydrocarbons of similar molecular weight. Moreover, the hydrogen atom in the $-COOH$ group can be released as a proton ($H^+$), which is why carboxylic acids are classified as acidic. This property is reflected in the term ‘carboxylic acid’.

Some common examples of carboxylic acids include acetic acid (commonly found in vinegar), citric acid (present in citrus fruits), and lactic acid (found in sour milk and produced in muscles during intense physical activity). All these compounds share the fundamental characteristic of the carboxyl functional group, which is responsible for their acidic nature.

In summary, the defining functional group of carboxylic acids is the carboxyl group, $-COOH$. This group is crucial for the distinctive properties of carboxylic acids, particularly their acidity and ability to form hydrogen bonds.