In analog design, the band gap (or energy gap) is the energy difference between the top of the valence band and the bottom of the conduction band in semiconductors (ie your process).
As you might be aware, for silicon, this is between 1.23-1.26V. In this context, and for the past decades the bandgap reference has been extensively used in order to provide an accurate voltage, by using the difference of two forward-biased diode junctions to generate a PTAT.
In the past couple of years however, many institutions and yes, including universities have forseen a little problem with this approach. As we scale down our technology processes, you will find that so does our supply (ie less than 1.2V). So simply to answer your question, non-bandgap references are recent efforts to resolve a voltage reference below the bandgap of the process.