Wheel turning king runs the country without stick or sword, what does it mean?
I believe "wheel" refers to tradition (in the broadest sense) and "turning" refers to establishing and/or continuing the tradition.

The wheel turning king (or, in modern terms, leader) rules by setting up a way of doing things that (most of) people find compelling enough to follow, without being forced to -- this is what I feel is referred to as "without stick or sword".