An input dictates where the signal is coming from and an output is where the signal is going to go afterward.
Common input devices include Cd Players Ipods and Vinyls, that produce an electrical signal that can be put in , or inputted into the mixer to be amplified and transduced from an electrical pulse into a sound wave.
Music sources are considered inputs devices because they are plugged into the input section of the mixer. This section is on the back of of the mixer, and corresponds with the channels. Each channel will have an independent input section usually designed with two levels of input called Line and Phone.
An output dictates where you want to send the signal once it has been processed by the mixer. A DJ mixer usually has two sets of outputs, and also a headphone output.
One that ends up at the audience called a master output and a Booth Output. These output signals are the similar, but they will generally have separate volume controls.