Hi Sharas
That means that if you put a pure sinusoidal signal of some frequency at the input, the output is a sinusoid of the same frequency, with some aplitude and whose phase advances the output. Pure sinusoidal means that it does not have a start, it comes from t=-infinity.
It you start to apply the sinusoid at some time, the ouput has a transient and after some time (when the transient has extinguished enough) you see the steady state: the output phase "advances" the input.
There is no violation of causality. The output "advances" bacause of all the history. If the input has a change (for example, if it stops or abruptly changes its phase, its ampltude or its frequency) that is not forecasted in advance at the output. That produces another transient, after which the ouput reaches the new staedy state.
I hope this helps you
Regards
Z