How can functional groups be bounded?
Functional groups are a unifying idea in organic chemistry. There are tens of millions of different organic chemicals but many of their key properties are determined by the functional groups they contain. For example, amines (compounds with the $\ce{-NH2}$ group) are basic and often smelly; carboxylic acids (containing the $\ce{-COOH}$ group) are acidic. 

The bar in the symbol represents the bond to the rest of the molecule. Sometimes chemists write this slightly differently by including a specific symbol for the rest of the molecule like this: R-OH where R is the rest of the alcohol. So a chemist might talk about a series of similar alcohols by defining R as $\ce{CH3}$ (methanol) $\ce{CH3CH2}$  (ethanol) or $\ce{(CH3)2CH}$ (isopropanol).

This simplifying terminology allows chemists to talk about large groups of related compounds without having to be too verbose and writing out all the details of every structure.

This is an organic chemistry concept so the functional group attaches covalently to a carbon. Some groups can also occur in inorganic compounds but the terminology would be different. For example, Sodium Hydroxide contains an isolated OH but this isn't an alcohol and wouldn't be written or described using terminology related to functional groups.