The blue curve you see above represents the graph of a function u(x,t) for a fixed value of t.
The coordinate x varies in the horizontal direction. The left side of the white frame corresponds to x=0, and the right side to x=1. The top of the white frame corresponds to the level u=1, and the bottom to u=-1. The level u=0 is right in the middle.
When you click "Start", the graph will start evolving following the finite difference scheme specified above.
Check also the other online solvers