This shows a path homotopy between two loops in the torus $T=S^1\times S^1$. The initial loop is $u*v$, where $u$ is the horizontal red circle and $v$ is the vertical blue circle. By sliding the slider we see that this is path homotopic to $v*u$. (It is an unusual feature of the torus that $\pi_1(T)$ is commutative. In most other spaces, $u*v$ would not be path homotopic to $v*u$.)