Most logical explanation is that Neandertals were descended from a previous expansion out of Africa, isolated for 100,000 years or more, developing over this time their distinctive genome.
Modern humans moved out of Africa, displacing or exterminating Neandertals, though mixing with them to a minor extent.
What is reasonably obvious is that those who left Africa were subjected to new evolutionary pressures, those who stayed were not, or at least not to the same extent.
I leave it to others to speculate how this might have affected evolution of increased intelligence and other traits.
Thank you for replying, and for explaining in layman’s terms.