Discrete Time Signal Property Property:

The frequency of oscillation of discrete time sinusoids sequence increases as $\omega$ increases from $0$ to $\pi$. If $\omega$ is increased from  $\pi$ to $2\pi$ then frequency of oscillation decreases.

My question:

What is meant by "frequency of oscillation" ?

How can a frequency of a signal vary (increase) from $0$ to $\pi$ and (decrease) from $\pi$ to $2\pi$. Isn't it should be same from $0$ to $2\pi$ ?
I think it means the "apparent" frequency of oscillation. It's poorly worded.

What's happening is that the frequency is increased to the Nyquist rate in the first half and then above it, causing aliasing, in the second.

What looks like the frequency increases in the first half and decreases in the second because of aliasing.