Conquest is the act of conquering a country or group of people.

Conquests are lands that have been conquered in war.

If someone makes a conquest, they succeed in attracting and usually sleeping with another person. You usually use conquest when you want to indicate that this relationship is not important to the person concerned.

You can refer to the person that someone has succeeded in attracting as their conquest.

The conquest of something such as a problem is success in ending it or dealing with it.