This is a multiplayer achievement and can only be done in ranked matches.
To win a Territory Control match, your team has to have control of the territory longer than the opposing team. To get control of the territory, people from your team have to be around the territory with any enemies around. The territory gets moved periodically throughout the match. It is shown on the map as a white symbol when the territory just got moved, a blue symbol if the MI-6 team has control, an orange symbol if the Organization team has control, or a half-blue, half-orange symbol if neither team has control. The territory is shown as a circle in you map in the top right corner of you screen and if you are looking in the direction of the territory, the symbol will appear on your screen.
If you need help with this achievement, please use the Quantum of Solace Achievement Trading Thread.