The study centers on the name "Charlie," which, 100 years ago, was almost exclusively a name for boys. In 1910, only 5% of Charlies were girls. Now, 51% are female.
The research organizes a name by giving it a score based on how gendered that name is. A name that is used exclusively for one gender, something like Julia, for instance, has a score of 1. A name that's perfectly neutral, like Sam, has a score of 0. So the smaller a score is between 0 and 1, the more neutral it is.
The mean score for names overall in 1920 was 0.97--pretty gendered. Now, in 2016, the last year for which the SSA has data, the score has dropped to .946. It's not a huge decline, but considering the scale of data it means there are many, many more gender neutral naming choices being made.
Besides Charlie, other names whose gender scores have signifcantly dropped include Skyler, Casey, Parker, and Alexis.
Conversely, some names have become more gendered: Ashton, which used to be pretty neutral, is now mostly a boys' name. Harper used to be more common for boys and is now much more common for girls.