The explanation below is not exact, and several aspects of how this works differ between different systems (and maybe even the same OS on different hardware for some portions), but I think that it is generally good enough for you to satisfy your curiosity enough to use them. Most people start using signals in programming without even this level of understanding, but before I got comfortable using them I wanted to understand them.
signal delivery
The OS kernel has a data structure called a process control block for each process running which has data about that process. This can be looked up by the process id (PID) and included a table of signal actions and pending signals.
When a signal is sent to a process the OS kernel will look up that process's process control block and examines the signal action table to locate the action for the particular signal being sent. If the signal action value is SIG_IGN then the new signal is forgotten about by the kernel. If the signal action value is SIG_DFL then the kernel looks up the default signal handling action for that signal in another table and preforms that action. If the values are anything else then that is assumed to be a function address within the process that the signal is being sent to which should be called. The values for SIG_IGN and SIG_DFL are numbers cast to function pointers whose values are not valid addresses within a process's address space (such as 0 and 1, which are both in page 0, which is never mapped into a process).
If a signal handling function were registered by the process (the signal action value was neither SIG_IGN or SIG_DFL) then an entry in the pending signal table is made for that signal and that process is marked as ready to RUN (it may have been waiting on something, like data to become available for a call to read, waiting for a signal, or several other things).
Now the next time that the process is run the OS kernel will first add some data to the stack and changes the instruction pointer for that process so that it looks almost like the process itself has just called the signal handler. This is not entirely correct and actually deviates enough from what actually happens that I'll talk about it more in a little bit.
The signal handler function can do whatever it does (it is part of the process that it was called on behalf of, so it was written with knowledge about what that program should do with that signal). When the signal handler returns then the regular code for the process begins executing again. (again, not accurate, but more on that next)
Ok, the above should have given you a pretty good idea of how signals are delivered to a process. I think that this pretty good idea version is needed before you can grasp the full idea, which includes some more complicated stuff.
Very often the OS kernel needs to know when a signal handler returns. This is because signal handlers take an argument (which may require stack space), you can block the same signal from being delivered twice during the execution of the signal handler, and/or have system calls restarted after a signal is delivered. To accomplish this a little bit more than stack and instruction pointer changes.
What has to happen is that the kernel needs to make the process tell it that it has finished executing the signal handler function. This may be done by mapping a section of RAM into the process's address space which contains code to make this system call and making the return address for the signal handler function (the top value on the stack when this function started running) be the address of this code. I think that this is how it is done in Linux (at least newer versions). Another way to accomplish this (I don't know if this is done, but it could be) would be do make the return address for the signal handler function be an invalid address (such as NULL) which would cause an interrupt on most systems, which would give the OS kernel control again. It doesn't matter a whole lot how this happens, but the kernel has to get control again to fix up the stack and know that the signal handler has completed.
WHILE LOOKING INTO ANOTHER QUESTION I LEARNED
that the Linux kernel does map a page into the process for this, but that the actual system call for registering signal handlers (what sigaction calls ) takes a parameter sa_restore parameter, which is an address that should be used as the return address from the signal handler, and the kernel just makes sure that it is put there. The code at this address issues the I'm done system call (sigreturn)and the kernel knows that the signal handler has finished.
signal generation
I'm mostly assuming that you know how signals are generated in the first place. The OS can generate them on behalf of a process due to something happening, like a timer expiring, a child process dying, accessing memory that it should not be accessing, or issuing an instruction that it should not (either an instruction that does not exist or one that is privileged), or many other things. The timer case is functionally a little different from the others because it may occur when the process is not running, and so is more like the signals sent with the kill system call. For the non-timer related signals sent on behalf of the current process these are generated when an interrupt occurs because the current process is doing something wrong. This interrupt gives the kernel control (just like a system call) and the kernel generates the signal to be delivered to the current process.
