The cohomology of the moduli space of curves has been a subject of interests to people from different fields for a long time. What are some interesting motivations to understand it?

Could anyone give some interesting motivations to understand the cohomology of $\mathcal{M}_g$?

What I know: I have read the various approaches to construct $\mathcal{M}_g$ via orbit spaces for group actions, period maps, and Teichmüller theory. I learned from literature that the cohomology of $\mathcal{M}_g$ is an important object to study, though I have not started reading some classical papers on the topic, such as Mumford's Towards an enumerative geometry of the moduli space of curves, Miller's The homology of the mapping class group, or Morita's Characteristic classes of surface bundles.

What aspects am I interested in: Some notes mentioned that the cohomology of moduli space is an important source of motives. Although I do not really understand what is a motive, any elaboration in this direction would be appreciated. Besides that, I am more interested in any concrete applications in algebraic geometry, differential geometry, or topology to motivate the study of cohomology of $\mathcal{M}_g$.