Not only exists the world that we live our lives but also the world of Forms (or Ideas) exists.
This is what Plato actually wanted to say.
The world of Forms is the true and real world. The world that we live is the world of shadows.
The world of Forms is the original world. The world that we live is the model world.
Therefore according to Plato, we must not cling to the world that we live now.
We must seek the world of Forms.
This is the way that we do philosophy.