Character UI is a way that people communicate with computers, machines that is by making interaction possible and straightforward as possible. Command-line interfaces are considered character UI’s and are a fine way of implementing scripts, programming or navigating the computer and software. They allow doing users to issue command lines to programs and software while these commands are text-based and not machine code or graphical. Most popular character UI’s would be MS-DOS and WCP (Windows Command Prompt).
On the other hand, graphical UI is everything the general public and we are accustomed today: interfaces, web pages, cursors, animations, you name it. Every method of interaction with software that is done by using a graphical component such as cursors, boxes, forms is an instance of a graphical UI. Humans as visual being tended to perceive things more quickly and are receptive to visual signals rather than other forms of communication, so it is only natural that we interact with technology this way.
The GUI is something introduced by Apple in 1983 in their first Mac but developed earlier by Xerox. And while the GUI is something that is for the general public, and something that most users enjoy, still, using a CUI is beneficial for high-level power users that need to do things in the most efficient manner.