A dangerous word, fat. It means large, or overweight, or — dare we say it? — even obese. If your brother has gotten fat, you might want to be tactful and call him "large-boned" instead.
Fat can be applied not just to people or animals, but to any inanimate object that is notably big. Dictionaries, for example (remember the old-fashioned printed kind?), are inevitably described as "fat tomes," or an engagement ring can be fat if the rock is big enough. In its literal sense, fat simply means flesh, a form of body tissue, and in this sense it doesn't imply anything excessive. Just be careful using it to describe certain people.