三 is the Chinese character for "three". It's often used on menus in the literal sense, for example to denote that a dish has three principal ingredients. One common use is 三鮮 (sān xiān), literally "three fresh", which usually refers to mixed seafood (e.g. prawn, squid, and scallops) — though don't confuse it with 地三鮮 (see below). Another is 三燒 (sān shāo), or "three roasts", which you might see as 三燒飯 (sān shāo fàn); three types of roasted meat served on rice.
If you read my post on 五/wǔ/five, you may remember that I mentioned 五花肉 (wǔ huā ròu/"five flower meat") as a name for pork belly. sunflower tells me that another name for this cut of meat is 三層肉 (sān céng ròu), or "three-layer meat".
三 is also used phonetically in the Chinese word for salmon: 三文魚 (sān wén yú). Note that the correspondence with the English word "salmon" is more apparent in Cantonese, where the first two characters are pronounced "sam men" (the final character, 魚, simply means "fish"). CantoDict tells me that the "formal" name for salmon is 鮭魚 (guī yú), but I've never seen this on a menu.
Here are some dishes with 三 in the name:
|三杯雞||sān bēi jī||three-cup [三杯] chicken [雞] (bone-in chicken braised with equal quantities of sesame oil, soy sauce, and rice wine)|
|地三鮮||dì sān xiān||"three fresh things from the earth" (deep-fried potatoes, peppers, and aubergines)|
|涼拌三絲||liáng bàn sān sī||three-sliver salad (a combination of bean thread noodles/粉絲/fěn sī and a couple of shredded vegetables)|
|三寶滑腸粉||sān bǎo huá cháng fěn||"three treasures" cheung fun|
|三鮮炒麵||sān xiān chǎo miàn||stirfried [炒] noodles [麵] with mixed seafood [三鮮]|
Finally, just for superpitching, I will note the existence of 三蛇羹 (sān shé gēng), or "three-snake soup", which according to CantoDict is a "famous Guangdong dish". This blog post has a little more information.
|三:||sān||radical 1 (一)||Cantodict||MandarinTools||YellowBridge||Zhongwen|