A dumb terminal has no processor. A server or mainframe does the computation for it. A "smart" terminal, or a personal computer, has a processor and does its own processing. It can also submit jobs to be processed by a server or mainframe, but it can stand alone as a non-connected (yet still "intelligent") machine.
A personal computer, such as a Dell desktop, an iBook, an Ubuntu Linux box, or any computer with a central processing unit (CPU) is a "smart" terminal.
The difference is that no processing is done at a dumb terminal... all the processing is done remotely at the server and the terminal is essentially just a screen and keyboard.
An intelligent terminal is far more common these days.