The Relic was/would have been the body of the Doctor.

Had the War occurred and the Doctor progressed in his adventures without the War encroaching on his past selves, he would have had many further adventures and accumulated a lot of knowledge and changes to his biodata.

Much of this information was lost during the ensuing war. Thus, when he died his body became very valuable to:

• The Time Lord from the War's future, because of what it contained and what they had so far lost in the war.
• Faction Paradox, as due to their methods biodata would be very valuable to them, especially such a well-lived specimen as the (future) body of the Doctor.
• Other parties, including UNISYC, Daleks, Krotons, and the Celestis.

The Relic was auctioned off by Mr Qixotl on Earth in the late 22nd century. The auction did not go to plan. The eighth incarnation of the Doctor arrived and ended up leaving with the Relic. He took it to the planet Quiescia and destroyed it. (PROSE: Alien Bodies)