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What is “automatic stack expansion”?

getrlimit(2) has the following definition in the man pages:

RLIMIT_AS The maximum size of the process's virtual memory (address space) in bytes. This limit affects calls to brk(2), mmap(2) and mremap(2), which fail with the error ENOMEM upon exceeding this limit. Also automatic stack expansion will fail (and generate a SIGSEGV that kills the process if no alternate stack has been made available via sigaltstack(2)). Since the value is a long, on machines with a 32-bit long either this limit is at most 2 GiB, or this resource is unlimited.

What is meant by "automatic stack expansion" here? Does the stack in a Linux/UNIX environment grow as needed? If yes, what's the exact mechanism?