A strategy game term. A tech tree is a tree structure that determines what buildings/technologies you need in order to be able to build/research other buildings/technologies. It is perhaps best described by an example:
The Protoss technology tree from Starcraft
Pylon Nexus Assimilator
|
/ \
/ \
Gateway Forge
| \
/ \ \
/ \ \
Shield Cybernetics Photon
Battery Core Cannon
|
_________|________
| | |
| | |
Citadel Stargate Robotics
of Adun | Facility
| | |
| | |___________
Templar /| | |
Archives / | Robotics Observatory
| / | Support
| / | Bay
| / |
| / |
Arbiter Fleet
Tribunal Beacon
So, for example, you first need a Nexus building in order to be able to build a Gateway, and a Cybernetics Core to build a Stargate. The Nexus is therefore called the prerequisite of the Gateway. The above diagram is included in the Starcraft package as a printed reference. Of course, serious players of Starcraft will have that thing memorised backwards.
However, this is a rather small tech tree. The tree for Sid Meier's Alpha Centauri has some 75 nodes with far more complex interlinks. (I refrain from displaying it here for the sake of ever getting this writeup done.) The tech tree in Alpha Centauri is not about buildings, however, but rather about actual technologies - about concepts like "Biogenetics" or "Industrial Economics". Having discovered such a technology gives you the ability to build certain buildings, units or "secret projects". So in order to research "Intellectual Integrity" you first need to know "Ethical Calculus" and "Doctrine:Loyalty". Such a structure is also called a research tree.
By the way, the expression tech tree isn't entirely correct, since in true tree structures, the branches don't grow together again. This does happen in tech trees. In the Starcraft example, two branches coming out of the node "Cybernetics Core" eventually rejoin at the leaf "Arbiter Tribunal". Another difference is that there may be several root nodes, i.e. several technologies/buildings that can be researched/built without a prerequisite. (in the example: Pylon, Nexus and Assimilator) This departure from rigid tree structure serves to make the technology tree more interesting.