Moore machine for LED display
State machines have an input that by convention isn't explicitly mentioned on the state diagram: the clock. In your case, it appears that what you call "the toggle button" is used to generate the clock.

This state machine has (according to the diagram) another input that you haven't mentioned, called Dir. This input and the current state determine what state the machine transitions to on each clock event. 

This state machine has 5 outputs. Four outputs control the 4 LEDs. The 5th output probably controls some other logic that produces the Dir input. Seeing what text is attached to the arrow pointing in from the right side of your image snippet might make this more clear. 

All the bits indicated below the line in each state bubble indicate outputs, not inputs.


  The input is connected to a toggle: 0001,1 &lt;- This 1 represent toggling the input


I would read it as a fifth output, not an input. Inputs should be marked along the lines, so you know what combination of inputs causes which transition.

Consider what you'd do if you had a more complex state machine with more than two possible transitions out of some of its states. Or with more than two transitions in to some of the states. You might even use a different set of inputs to get to state C from state A than you use to get to C from B. In that case putting the inputs needed to enter the state inside the state bubble would be very confusing.