# Flattened band in band structure

What does a flattened band in a band structure plot imply? I've been reading this paper https://doi.org/10.1016/j.apsusc.2012.06.092 and one of the primary results is the flattening of bands however it does not say anything about the significance of the band flattening. can anyone help me with this?

A derivation of the dependence of the band width on the nearest neighbor hopping (and an introduction in general) can be found in "Crystal-Field Theory, Tight-Binding Method and Jahn-Teller Effect" by Eva Pavarini (the bandwidth dependence (the factor $$2t$$ in front of the cosine) is introduced on pages 6.25/6.26).