If the Linux kernel determines that an unblocked signal is pending for a process, then, at the next transition back to user mode in that process (e.g., upon return from a system call or when the process is rescheduled onto the CPU), it creates a new frame on the user-space stack where it saves various pieces of process context (processor status word, registers, signal mask, and signal stack settings).
The kernel also arranges that, during the transition back to user mode, the signal handler is called, and that, upon return from the handler, control passes to a piece of user-space code commonly called the "signal trampoline". The signal trampoline code in turn calls sigreturn().
This sigreturn() call undoes everything that was done—changing the process's signal mask, switching signal stacks (see sigaltstack(2))—in order to invoke the signal handler. Using the information that was earlier saved on the user-space stack sigreturn() restores the process's signal mask, switches stacks, and restores the process's context (processor flags and registers, including the stack pointer and instruction pointer), so that the process resumes execution at the point where it was interrupted by the signal.
sigreturn() exists only to allow the implementation of signal handlers. It should never be called directly. (Indeed, a simple sigreturn() wrapper in the GNU C library simply returns -1, with errno set to ENOSYS.) Details of the arguments (if any) passed to sigreturn() vary depending on the architecture. (On some architectures, such as x86-64, sigreturn() takes no arguments, since all of the information that it requires is available in the stack frame that was previously created by the kernel on the user-space stack.)
Once upon a time, UNIX systems placed the signal trampoline code onto the user stack. Nowadays, pages of the user stack are protected so as to disallow code execution. Thus, on contemporary Linux systems, depending on the architecture, the signal trampoline code lives either in the vdso(7) or in the C library. In the latter case, the C library's sigaction(2) wrapper function informs the kernel of the location of the trampoline code by placing its address in the sa_restorer field of the sigaction structure, and sets the SA_RESTORER flag in the sa_flags field.
The saved process context information is placed in a ucontext_t structure (see <sys/ucontext.h>). That structure is visible within the signal handler as the third argument of a handler established via sigaction(2) with the SA_SIGINFO flag.
On some other UNIX systems, the operation of the signal trampoline differs a little. In particular, on some systems, upon transitioning back to user mode, the kernel passes control to the trampoline (rather than the signal handler), and the trampoline code calls the signal handler (and then calls sigreturn() once the handler returns).
The original Linux system call was named sigreturn(). However, with the addition of real-time signals in Linux 2.2, a new system call, rt_sigreturn() was added to support an enlarged sigset_t type. The GNU C library hides these details from us, transparently employing rt_sigreturn() when the kernel provides it.