what do this mean in guitar tabs?

I would have to see "//" in context to know what that means. 0 means open, meaning, you don't hold down that string.

// generally means "Same is the previous bar". For example if you're playing a chord in a certain rhythm in the previous bar, you repeat it in the bar that is marked with //

However in some rare occasions it could mean slide, depending if there are numbers in front and after.

A "0" means playing the open string of the noted.

A / sign means an acending slide and the note 0 is just that string played open