What is this extra divider line on my Dock? Mysteriously, this extra divider-line has appeared between any app I launch now and the previously launched apps? 

What is the purpose of this 2nd divider line? Why is it appearing now? How can I get rid of it?

See this screenshot, with pink arrow pointing to the mystery divider-line.
Recent apps

This is recently-opened applications, which is on by default in macOS Mojave. To disable, open System Preferences > Dock, and uncheck Show recent applications in Dock.