It depends on the context. TD (Technical Director) or TM (Technical Management) varies from industry to industry.
As far as theatre goes, a TD will often look over all drawing and plans to make sure that everything will work together - ie will the set get through the loading dock doors and onto the stage, and when it is there, will it actually fit under the lighting bars with the 12foot droppers and Mac500's on them etc. And will LX's rig draw too much power etc. Basically, the TD is the overseer of all things technical, and they should "slot in" at the start of production (attending all production meeting) and come into their own during bump-in. Whilst we tend to look after the human side of things until tech, the TD should look after the technical aspects.