From LQWiki

A warm boot is the act of restarting (rebooting) a computer that is already turned on, via the operating system. A warm boot is sometimes necessary when a program encounters an error from which it cannot recover. On linux computers, you can perform a warm reboot by switching to runlevel 6:

# init 6 

The 'reset' button usually will perform more or less the same function, although it is possible that some hardware will be reset differently.

A warm boot is also sometimes referred to as a soft boot. The opposite is a cold boot, turning a computer on from a powered off position.