This means that all possible or potential system states are equally probable. After measurement, the system is found in one, or a few states. Unfortunately, the founders left the philosophical picture at that, never examining what the lower level of existence, potentiality, really meant. In taking up this question, the context is generalized from physics to the philosophy of physics and experience in general. In order to address Muller's concerns with quantum weirdness, let me lay out the generalized philosophical basis of potentiality.
Perception requires sensing some difference.
If there is no difference present, nothing will be perceived. Let's take one paragraph at a time. The physicist chooses which invariance symmetry to break, either a wave type or a particle type. Our cultural, conceptual model of the world is built up through the historical sequence of symmetry breakings that accrue a picture of properties of the world. Any properties requires some symmetry breaking in my view.