Apache grinds to a halt and dies!

What exactly does this mean?  Does it run out of memory, or use too much CPU or I/O to finish the requests in time, or segfault (wrt the "dies"), or something else?  If it's CPU, how many requests (on average) do you need to handle per second?

I'm not asking "just because". Rather, I think a better understanding of what exactly the problem is, is essential for choosing an appropriate strategy to cope with it...