Today I want to talk about potatoes. The Mandarin Chinese word for potato is 土豆 (tǔ dòu), which literally means "bean of the earth"; I've posted about 豆/dòu/bean before, so the only new part here is 土/tǔ, which has a number of meanings including soil/earth/land. It's very rare to see 土 on a menu without 豆.
Potatoes play a rather different role in Chinese cuisines than in Western ones; rather than being a staple carb, they're treated like any other kind of vegetable. One consequence of this is that the potatoes themselves are often rather undercooked to Western tastes, particularly when served as 土豆絲 (tǔ dòu sī), or shredded potatoes, a crisp stirfry of finely-julienned potatoes cooked only very briefly to preserve the natural crunch of the vegetable.
"Undercooking" is not the only aspect that may confuse those more familiar with potatoes as a bulky side dish. Rather than being quite bland and served with a more flavourful protein or other "main" dish, a Chinese potato dish will often be deeply flavoured and even relatively spicy, and will generally be served with rice. Fuchsia Dunlop has an anecdote and some history relating to this — the comments are worth reading too, as is the Washington Post article she links to.
Another example of a dish that includes potatoes is 大盤雞 (dà pàn jī/big-plate chicken), a dish from Xinjiang in the northwest, which I posted about last week. Potatoes also appear in 地三鮮 (dì sān xiān), or "three [三] fresh [鮮] things from the earth [地]", a Dongbei (north-east Chinese) dish of aubergines, potatoes, and green peppers, all fried separately and then braised together in a savoury sauce.
Most of the Chinese potato dishes I'm familiar with, like those above, come from the cuisines of north/northeast/northwest and central China, rather than the provinces nearer the south/east/southeast coast. The ever-informative sung tells me in comments that this is because sweet potatoes and taro are more common than actual potatoes in the areas around the coast — and although potatoes are used in Cantonese home cooking, particularly in casserole/hotpot dishes, you're unlikely to see these dishes on a menu.
The Cantonese word for potato is 薯仔 (syu zai). This word isn't used in Mandarin, but the individual characters are; for example, the Mandarin for sweet potato is 番薯 or 蕃薯 (both pinyinised as fān shǔ).
For more thoughts on potatoes, see the eGullet thread on potatoes in Chinese cooking.