A system crash can mean any number of things, and it can also be caused by many different factors.
Probably the most common is when your computer just locks up, forcing you to reboot using the power/reset button. This is often known as the computer "crashing". This usually happens when too many applications are running at the same time; a collision of bits happens within the processor and the computer ceases to continue operating.
More serious "crashes" (as in, when the computer won't switch back on properly) can be caused by corruptions in the core operating system files. In windows, this often leads to a BSoD (Blue Screen of Death), in which an error code is given. The operating system can be corrupted by viruses, bugs in programs, or just the user modifying/deleting files that are required, such as elements in the Windows Registry.
Another factor that can cause a BSoD is the CPU overheating. This is more of a hardware problem, as the CPU either has dried thermal paste, or the heatsink is not properly attached.
If a computer fails to start after crashing, most Operating Systems have a "Safe Mode", which can be accessed by pressing certain function keys when the computer is booting, (usually F10). In safe mode, the operating system only loads the necessary drivers and files, therefore any viruses or programs affecting the operating system will not start. This allows the user to remove anything stopping the computer from functioning properly.
If, in Windows, the operating system has become corrupted, a Windows repair disc, with recovery console (downloadable from the microsoft website) can be used to restore any files that have been broken. The operating system should then boot up fine.