What is “spectral turnover”?

It just means, that when you look at the spectrum on a log-log plot, that it become flat or even reverses slope, in contrast to a steeper power law spectrum at higher and/or lower frequencies.

There are various physical reasons why a turnover might appear in the spectrum (e.g. a flattening in the underlying power-law distribution of electrons producing synchrotron emission or synchrotron self-absorption).

I was quickly able to find the following sketch (from this website) of a "GHz-peaked radio galaxy", which illustrates and explains the situation.