What is a mealy tomato, and how would one use one?
Yup, tomatoes can most definitely be a bit grainy. It's not a hard graininess like sand, but a softer graininess. The best comparisons that come to mind are hydrated but uncooked cornmeal or slightly wet breadcrumbs. Instead of being juicy and smooth (whether firm or soft), you'll notice a bit of small texture. It'll probably also be less juicy, and the flavor may not be as fresh and full as you'd like. If you've never had one, awesome - you've had good tomatoes!

It's also a common texture in some varieties of apples, especially when not too fresh. It's especially noticeable there; instead of a crisp crunch as you bite through it'll feel a little crumbly.

They'd be all right for things where you're going to cook them thoroughly so you won't notice the texture, like spaghetti sauce, though again the flavor may suffer as well. For anything remotely fresh, they're still edible, just noticeably not as good.