The Wiktionary definition isn’t bad.

First and foremost, car-brain refers to the individual expression of a sociological problem more formally known as "motornormativity". It’s the state of being unable to envision a world different from the one we currently live in, where everything gets designed around cars to the exclusion of more efficient forms of transport like public transportation and cycling. It’s an opposition to the idea of walkability in practice, if not necessarily in theory (someone might say they like walkability, but then oppose specific measures which would increase walkability, like zoning changes, increasing footpath width by decreasing road width, decreasing speed limits, and adding modal filters).

It’s also the tendency to blame "pERsoNaL rESPoNsibiLiTy" for traffic crashes, and disregard systemic issues that lead to increased chances of crashes occurring. But also to excuse the personal behaviours that cause the crash to happen in other circumstances, while being overly critical of non-drivers exhibiting the same behaviours. Any time you see someone say "cyclists ignore stop signs and run red lights!" That’s motornormativity, and the individual saying it is deeply car-brained. Especially if they do it in a context of talking about better cycling infrastructure or pro-cycling laws, as a way to imply "no, we shouldn’t make things better for cycling". Not only do studies suggest cyclists break the law at roughly the same rate as drivers (yet you never see these people complain about all the drivers who do it and suggesting that therefore we should make driving harder), we also know that when cyclists break the law, they’re far less likely to endanger others than drivers are; indeed, cyclists who break the law frequently do it to increase their own safety, while drivers break the law to increase their own convenience.

That’s only a small slice of how motornormativity presents in our society, but hopefully it’s a good enough primer. Here’s a pretty good article on the subject.