:) - that is a smiling face. :D - that is a laughing face. :( - that is a frowning face. :| - that is a straight face. Now, imagine someone has told a really funny joke - but you're at a funeral. You want to laugh, but you're at a funeral. So instead of having a laughing face :D, you try to keep a straight face :|. Or, imagine your boss is doing something very embarrassing. If you smile :), she will fire you. So, you need to keep a straight face :|. That's keeping a straight face - not laughing or smiling when it might be inappropriate to laugh or smile.

To keep a straight face is to have a blank or serious facial expression, especially when trying not to laugh.