An undershirt is a piece of underwear worn against the skin, under your shirt. It may have short sleeves or no sleeves at all. Its job is to keep you warm, to soak up sweat so your outer shirt stays clean, and to stop a thin shirt from showing your skin. The important thing for you to know is that this is the American word. British English calls the same thing a vest — which causes real confusion, because in American English a vest is the sleeveless thing you wear OVER a shirt as part of a three-piece suit (British: waistcoat). So one word, two opposite layers, depending on which side of the Atlantic you are on. In Taiwan you will hear 'undershirt' more often, because American English dominates in schools here. Everyday speakers also have nicknames: a plain white sleeveless one is called a tank top (US) or, rudely, a 'wife-beater' — that last one is genuinely offensive and I would not use it. Note the spelling is one word, no hyphen.

內衣、汗衫（穿在襯衫裡面那件）。台灣男生說的「衛生衣」冬天版、無袖的「背心內衣」都算。英式英語叫 vest。