According to the government policy for traveling in Tibet, visiting some remote areas or sensitive border areas only with the TTB permit is not enough. Military Permit is additionally needed if your itinerary includes Ngari (Mt. Kailash, Lake Manasarovar, etc), Nyingchi (Pomi, Rawu, etc.) and some places in Shannan area. For Tholing and Tsaparang in western Tibet, you will also need a permit from the local Cultural Antiquities Department.
Besides of the places mentioned above, the overland tours to Lhasa from Sichuan, Yunnan, Qinghai or Xinjiang also require a Military Permit. And most importantly, you are going to need the military permit before you start your overland tour, not upon your arrival in Lhasa.
The Military Permit is applied through travel agency before you enter Tibet and is issued by the military office in Lhasa. It is absolutely needed for travel to Ngari, Nyingchi (outside Nyingchi township) and Chamdo (Sichuan and Yunnan to Tibet overland tours pass by), which are regarded as military sensitive areas.
The Military Permit arrangement procedures take about 2 weeks, so if one of those sites is included in your travel itinerary, you are highly suggested to plan the trip at least 30 days prior the departure date.
What does a Military Permit look like: