A darwinist is one who holds to the evolutionary story. It is a description of history that attempts to explain how we have emerged to be rational, moral, conscious human beings through natural selection and laws of nature. A materialist holds to a set of presuppositions that imply that reality is fundamentally reducible to what is physical. Nagel says that darwinistic materialists are committed to a set of presuppositions (a constitutive account) that is reductionary (all is physical) and a story (a historical account) that is emergent (all that is emerged through natural selection). His gripe with this combo is that neither the constitutive account nor the historical account can account for human consciousness. Consciousness is neither purely physical (and cannot be reduced to physicalism without absurdities like panpsychism) nor is it emergent (it implausible that consciousness could emerge through natural selection).
Thomas Nagel argues that if you are committed to a reductive materialism/physicalism and a darwinistic historical narrative you have a problem – consciousness.
Nagel’s very tentative suggestion is to tackle the problem historically. He suggests that while there is no intentional mind governing the emergence of human life, there may well be some teleological thread yet to be woven into the darwinist account. He admits that this is quite speculative, but is convinced that if those committed to darwinistic materialism don’t come up with something the whole worldview is prone to collapse.