The technology race refers to researching technologies and getting to the later eras as quickly as possible. It's good to keep up with everyone in the tech race, as you will be less likely to get attacked. It's even better to be ahead of everyone else, as it gives you advantages. However, all of the other civilizations will try and squeeze tech out of you by demanding it. In case of this, remember that you have an advantage: with your higher tech level, you can mass-produce advanced units. So, if they do make a demand, you can reject their "generous offer" and risk war. You can defend yourself by recruiting new advanced units to defend your cities. The demanding civilization will either go away or declare war on you. This is when having a big civilization, large armies, and wealth can come in handy.