Each member sets their own green check marks.

only you see the green check marks when you set them,

they are the threads that you have marked "subscribed to"

to subscribe you click on thread options then subscribe. to make the green check mark go away you click on that threads options and click "unsubscribe"

subscribe makes it easy for you to find the threads you are interested in going to quickly.

you access your subscribed threads list in your profile options edit subscribe.

I use subscribe often for threads I have started and those that I want to go back and read again or keep track of.