ELI5: Explain Like I'm 5

Continuous linear operator

A continuous linear operator is like a machine that adds two numbers together. It takes two inputs, x and y, and it adds them together to give you a result. It doesn't matter what the two numbers are, it just adds them together. The important part is that the machine does the same thing every time, no matter what the inputs are. So if you put in the same two numbers over and over, the machine will always give you the same result.