It means to rethink something, regardless of whether or not you end up changing your mind. an example could be: You're the head of an R&D department, someone comes up with an idea, after thinking about it for a little while, you dismiss it. A few days later, they bring you the same idea, perhaps with a few revisions, or a better argument as to why you should put the time and effort into it, and you think about it again. You're giving it a second thought. hope that helps