Technologies are upgrades for your regular troops stationed in the Command Center. Each Technology adds a certain amount of life and damage points to a specific soldier. In order to be able to Research the Technology, your clan must have a certain amount of Influence Points that it received in the captured territories.
If you have gained access to a specific Technology, Researched it, and then your clan lost all its Influence, the Technology will no longer be active. Your clan must re-earn Influence points, and then the Technology will become active again (you do not have to Research it again).