The word "crunch" can be used informally to mean "time pressure" or performance pressure in general.
"He seems to be very good, but I don't know yet if he can perform in the crunch."
In the context of a technology project, "crunch" often refers to the situation in which a project is behind schedule but needs to be completed by a deadline anyway.
I don't know for sure, but when I hear the word "crunch" I think of a project chart with lines on it that used to stretch out for weeks and now are going to get squeezed together and "crunched."
"I'm sorry, sweetie, we have to postpone our vacation; it's crunch time at work and we'll be working overtime through the end of the month."
The website name "TechCrunch" doesn't mean anything in particular. They were obviously just trying to invent a name that a) wasn't already in use, and b) sort of suggests "technology" and "news," and c) carries a feeling of excitement or energy, and some feeling of being "cool" or "hip." It could just as well have been "TechBuzz" or "TechScoop" or "TechBang."