Indecorous behavior isn't proper or socially acceptable. It would be indecorous to publish your sister's diary in the newspaper or to tell your extended family an offensive joke at Thanksgiving dinner.
Rude or off-color remarks are indecorous, and wearing a bikini to a formal dinner would also be indecorous. Indecorous things lack decorum, which is good manners or proper behavior. Indecorous, from the Latin decorus, "becoming or seemly," comes from the root word decus, "ornament," and is related to words like "decorate" and "decent."