Most programs need to allocate storage dynamically in addition to whatever static storage the compiler reserved at compile-time. To C programmers this fact is rather obvious, but for many years this was not an accepted and recognized fact, and many languages still used today don't support this notion adequately.
The classic UNIX kernel provides two very simple and powerful mechanisms for obtaining dynamic storage, the execution stack and the heap. The stack is usually put at the far upper end of the address-space, from where it grows down as far as needed, though this may depend on the CPU design. The heap starts at the end of the bss segment and grows upwards as needed.
There isn't really a kernel-interface to the stack as such. The kernel will allocate some amount of memory for it, not even telling the process the exact size. If the process needs more space than that, it will simply try to access it, hoping that the kernel will detect that access have been attempted outside the allocated memory, and try to extend it. If the kernel fails to extend the stack, this could be because of lack of resources or permissions or because it may just be impossible to do in the first place, the process will usually be shot down by the kernel.
In the C language, there exists a little used interface to the stack, alloca(3), which will explicitly allocate space on the stack. This is not a interface to the kernel, but merely an adjustment done to the stack-pointer such that space will be available and unharmed by any subroutine calls yet to be made while the context of the current subroutine is intact.
Due to the nature of normal use of the stack, there is no corresponding "free" operator, but instead the space is returned when the current function returns to its caller and the stack frame is dismantled. This is the cause of much grief, and probably the single most important reason that alloca(3) is not, and should not be, used widely.
The heap on the other hand has an explicit kernel-interface in the system call brk(2). The argument to brk(2) is a pointer to where the process wants the heap to end. There is also a interface called sbrk(2) taking an increment to the current end of the heap, but this is merely a libc front for brk(2).
In addition to these two memory resources, modern virtual memory kernels provide the mmap(2)/mmunmap(2) interface which allows almost complete control over any bit of virtual memory in the process address space.
Because of the generality of the mmap(2) interface and the way the data structures representing the regions are laid out, sbrk(2) is actually faster in use than the equivalent mmap(2) call, simply because mmap(2) has to search for information that is implicit in the sbrk(2) call.