The EOF is a character (usually meant to signal if there aren't characters/bytes in a file left). You trigger this character by pressing Ctrl+D together, not as other characters whereby you just press one button (e.g. 'A'). This character is already defined just like all other characters, that's why you don't need to define it, as you don't need to define the letters 'A' or 'B' for example. In the program input, by clicking Ctrl+D you signal to the program that there isn't any input to give anymore (end of input, as you might want to visualize this). Wikipedia says this:
In computing, end-of-file (commonly abbreviated EOF) is a condition in a computer operating system where no more data can be read from a data source. The data source is usually called a file or stream.