This is fairly straightforward. I'm sure at some time in our lives we've sat with friends and discussed how to solve the world's problems (="putting the world to rights"). :)

It means that you sat around discussing the world's problems and what you'd do to solve them.

'Put/set the world to rights' is an idiom meaning 'to talk about how the world could be changed to be a better place.' 'We sit round the table, putting the world to rights.' 'We stayed up all night, setting the world to rights.

where this word come from? Give the text about it , so we can get the meaning from the context. The same word maybe have different meaning in different texts.