From my understanding, when a process is under execution it has some amount of memory at it's disposal. As the stack increases in size it builds from one end of the process (disregarding global variables that come before the stack), while the heap builds from another end. If you keep adding to the stack or heap, eventually all the memory will be used up for this process.
How does the amount of memory the process is given get determined? I can only imagine it depends on a bunch of different variables, but an as-general-as-possible response would be great. If things have to get specific, I'm interested in linux processes written in C++.