Tater means potato. It is not a different vegetable and not a special kind of potato — it is just what happens when people say 'potato' fast and drop the first bit: p'tato → tater. It is casual, warm, and regional. You hear it in the American South and Midwest, in parts of rural Britain and Ireland, and in country songs; it can sound folksy, homely, sometimes a bit jokey. You would not write it in an essay or a business email. There are a few fixed places it lives that a learner will genuinely meet. Tater tots are those small deep-fried cylinders of shredded potato — a very common American side dish, and the name is on packets in supermarkets, so it is not slang there, it is the product's name. In Britain, 'tatties' (the Scottish and northern form) turns up in food names too. Some older speakers also use 'small potatoes' or 'taters' figuratively for something unimportant, but that is uncommon and you can safely leave it aside. Note the spelling too: you will sometimes see it written 'tatter with an apostrophe at the front — 'taters — because the writer is showing you a missing sound.