We use this phrase to admit to changing our opinion after listening to another person’s further explanation. It suggests that we are admitting that we made a mistake and can now see that the other point of view is correct. It can be used in fun, casual ways, too.
A: Why did you throw that plastic on the ground? B: There were no trash cans around. Don’t worry. It’ll be fine. A: What?! It could blow into a lake and a poor duck could choke on it! B: Well, when you put it that way…I’ll pick it up. Sorry.
A: I shouldn’t eat any potato chips. I’m on a diet. B: Hey, potatoes are vegetables, and vegetables are good for you. A: Well, when you put it that way…can I have some?