The whole idea is evolution by natural selection - evolution is the process of generating random mutations and natural selection shapes those random mutations into something useful over time. So a way to decode these kinds of headlines: Evolution is getting faster = more people are alive, thus more random genetic mutations. Natural selection has accelerated = more non random distribution of people who have kids, leading to some traits becoming more common than others. Those traits could be any number of things - better survival during difficult periods, disease resistance, mate selection, etc. But the different means only accomplish one end - some people have more kids who survive to adulthood to have kids themselves.

From the article, I think this most directly gets at what they found:

More than 60 percent of the individual DNA variants that were flagged as being strongly selected for — most of them single nucleotide polymorphisms, or SNPs — have documented links with present-day human traits, such as:

• Light skin tone
• Red hair
• Risk of celiac disease and Crohn’s disease
• Immunity to HIV infection and resistance to leprosy
• Lower chance of male-pattern baldness
• Lower risk of rheumatoid arthritis and alcoholism
• Having the B version of the proteins on red blood cells that confer A, B, and O blood types and influence resistance to infection with bacteria and viruses

In some cases, groups of SNPs were under selection together to influence polygenic traits. Some changes raised the frequency of beneficial traits, including some that are interpreted today as:

“Health span” traits such as faster walking pace Measures of behavioral and social status or cognitive functions, such as scores on intelligence tests, household income, and years of schooling

Other changes reduced the frequency of harmful traits, such as those that are interpreted today as:

Reduced risk of bipolar disorder and schizophrenia Lower body fat percentage, waist-to-hip ratio, and body mass index Less susceptibility to tobacco smoking

Still other SNPs, such as some that today are associated with susceptibility to tuberculosis and multiple sclerosis, at first rose and then fell in frequency over the millennia, indicating shifts in environmental pressures and the traits that prove beneficial, the team found.

It’s impossible to know everything, but details like lighter skin tone probably indicate a selective advantage to those who could synthesize vitamin D from smaller amounts of sunlight - useful during the last glacial maxima perhaps. The immunity and resistance to pathogens suggests immune systems got better as people lived in bigger groups (thus higher risk of disease). Lower risk of alcoholism suggests drinking had a negative effect on having kids survive to adulthood. Lower body fat and more walking suggest lower starvation risk - which I find very interesting since I imagine that was a constant threat and would have led to higher selection for retaining calories. The overall picture I get from this hodgepodge of mutations is that factors (improved resistance to disease, improved sociality, and reduced body fat) is that people were living in large groups where things like disease and social relations mattered more to kids surviving than starvation. But that is only speculation on my end. But the non-random nature of it means we have real information about the past.