These curves are named "attractor"s because if the system is disrupted (say by throwing the pendulum in the air) it will soon return (be "attracted" back) to the path of its attractor.
It's not, of course, that the curve itself does any "attracting", just that following physical laws leads the system back to the attractor's path.

"Phase diagram" is the other name for a graph in which one variable is plotted against another (rather than against time) - because the shape of the graph shows how much one variable lags behind (or is "out of phase with") the other.
In the case of the pendulum, the circular shape of the position:velocity phase diagram shows  that their phase difference  is 1/4 cycle.