The usage of "Stable" vs "Latest" is unfortunately rather inconsistent (on the home page "Download Latest" refers to the latest stable 4.x version, on the docs "Latest" seems to refer to master branch), but basically the main reason for having an LTS is to support people who have invested a lot of time in a 3.x project and for whom porting to 4.x would be prohibitively time consuming.
A very similar thing happened when python 3 came out - there were a lot of breaking changes from python 2, so even though 3 was always recommended for new projects, the python developers supported version 2 for over 10 years after the release of 3 so that projects that didn't have the resources to port to the new version weren't abandoned.