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 $\mathcal{M}_g$.