Reboot means the same as restart.
(Some incorrectly say 'reboot' when they talk of completely wiping their PC and installing Windows all over again.)
It's given this name due to similar acts in the army (among other disciplines). Every time you switch your computer on, it starts up as though it was the first time. It checks for memory and processor, then checks for USB ports and other devices. This is much like booting up (i.e., fastening your boots in the morning), as it's like you're doing it for the first time each morning.
Sometimes installers and other programs that want you to restart present you with a button to click to restart. Other times you just get asked to do it, meaning you have to do it manually as you always do (Start -> Restart if you're on Windows, for example).