It's historically true that names almost always pass from being "boy names" to unisex to "girl names", with almost no names going in the other direction. That process is completed with Ashley, it's mostly happened to Leslie and Lindsey, and it's ongoing with Riley, Jordan, etc.

I think the graph implies that this process happens in the US and UK at different moments: Americans start giving boys' names to girls, and only later do Brits do the same. Possibly, Americans are very high-profile in media, so they have disproportionate influence on international trends?