The most common meaning would be 'willingly following social conventions'. It is maybe an antonym to 'anarchy'. 'Chinese government relies a lot on the conformity of its citizens'. It can also be used in a more physical sense: 'The fit of a dress relies a lot on the conformity of the fabric', where that refers to the fact that the fabric follows the shape of the wearer.

It means something like "being obedient to" "In Iran, I won't drink any alcohol in conformity with the muslim culture."

It has a range of meanings. The two that come first to my mind are social conformity, and conformity with specifications. "Social conformity" means a very strict adherence to social expectations or norms. For example, I could write, "In the United States, the 1950s were an era of social conformity. People tried to look alike and act like. Men were afraid to wear their hair long, women were afraid to wear pants instead of a skirt." "Conformity with specifications" would be the language of contracts, engineering, or purchasing. For example, "Thank you for your proposal. We will be reviewing all of the proposals we have received for conformity with our bid specifications, and expect to announce the results of the review before September 22th."