What is assembly bias in context of cosmology?

What is assembly bias in context of cosmology?

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I see the term "assembly bias" being used quite a bit in cosmology literature? I have not been able to find a good primer on what it means, and why it is important.

Early analytic calculations of the distribution of the masses of dark matter halos (in which galaxies reside) by Press & Schechter (1974), Bond et al. (1991), Mo & White (1996) and several others showed that the clustering of these halos depended only the redshift and the mass of the halos. However, later work showed that clustering depends on several other parameters, such as the assembly history of the halos (Sheth & Tormen 2004; Gao et al. 2005).

This fact is known as the assembly bias. I think the first to use the term was Croton et al. (2007). Later, the term was "expanded" to also refer to the dependence of the clustering on halo spin, concentration, and shape (ellipticity) of the halos.

You can find some more recent good discussions in Lazeyras et al. (2017) and Padilla et al. (2019).