Straight-faced means keeping your face completely still — no smile, no laugh — while you are saying something funny or something that is not true. The whole point is the gap between the face and the words. If a friend tells you, perfectly straight-faced, that he has bought an elephant, the joke lives in the fact that he did not smile. It is used both as a describing word before a noun ('a straight-faced reply') and after a verb ('she stayed straight-faced the whole time'). It is a compliment to the joker's skill: keeping a straight face is hard. You will see this written three ways — straightfaced, straight-faced, and as two words in the very common phrase keep a straight face. That phrase is the one your students will meet most: 'I couldn't keep a straight face.' The hyphenated straight-faced is the usual spelling of the adjective; write it that way and no one will mark you wrong. There is a slightly different flavour when it describes not a joker but a serious, unsmiling person or account — 'a straight-faced report' can just mean one delivered without any humour at all.

面不改色的、板著臉不笑的（尤其是在開玩笑或說假話的時候）。台灣口語會說「一臉正經地」「憋著不笑」；片語 keep a straight face 就是「忍住不笑」「憋笑」。