A more thorough explanation:

Definition: Notorious cohabitation refers to the act of living together as partners in life, usually with the suggestion of sexual relations, in a way that is considered questionable on grounds of social propriety, though not necessarily illegal. It can also refer to illicit cohabitation in which the parties make no attempt to hide their living arrangements.

Examples:

• An unmarried couple living together and engaging in sexual intercourse.
• A couple living together in a way that is considered scandalous by their community.

These examples illustrate the definition of notorious cohabitation as they both involve unmarried couples living together in a way that is considered socially unacceptable. While the first example is illegal in some places, the second example may not be illegal but is still considered questionable on grounds of social propriety.