In general, the events that generate signals fall into three major categories: errors, external events, and explicit requests.
An error means that a program has done something invalid and cannot
continue execution. But not all kinds of errors generate signals—in
fact, most do not. For example, opening a nonexistent file is an error,
but it does not raise a signal; instead, open returns -1.
In general, errors that are necessarily associated with certain library
functions are reported by returning a value that indicates an error.
The errors which raise signals are those which can happen anywhere in
the program, not just in library calls. These include division by zero
and invalid memory addresses.
An external event generally has to do with I/O or other processes. These include the arrival of input, the expiration of a timer, and the termination of a child process.
An explicit request means the use of a library function such as
kill whose purpose is specifically to generate a signal.
Signals may be generated synchronously or asynchronously. A synchronous signal pertains to a specific action in the program, and is delivered (unless blocked) during that action. Most errors generate signals synchronously, and so do explicit requests by a process to generate a signal for that same process. On some machines, certain kinds of hardware errors (usually floating-point exceptions) are not reported completely synchronously, but may arrive a few instructions later.
Asynchronous signals are generated by events outside the control of the process that receives them. These signals arrive at unpredictable times during execution. External events generate signals asynchronously, and so do explicit requests that apply to some other process.
A given type of signal is either typically synchronous or typically asynchronous. For example, signals for errors are typically synchronous because errors generate signals synchronously. But any type of signal can be generated synchronously or asynchronously with an explicit request.