To tech is to build tech buildings or research new technologies or upgrades, in order to build more advanced units and exercise later game strategies. Most units and abilities are not available at the beginning of the game, and players must tech to take advantage of them. But teching requires a large resource commitment, which can slow the player from taking the other main strategic choices like (expanding or attacking). Players are vulnerable to rushing before they are finished teching.
Teching pushes the game through it's early, mid, and late stages. In many racial matchups players will play very defensively and tech in order to push the game to a stage where their race has the advantage. Of course, the faster the player can tech, the quicker the chance he has access to more advanced units and thus a sooner time to attack his opponent.