This can be used in one of two ways. We’ll start with the nutritional science manner. Red meat is any type of meat that contains more of a particular type of protein than others. This protein is called myoglobin, and its primary function is as an iron and oxygen binding protein, usually found in the skeletal system tissues and cardiac tissues of vertebrates, including almost all mammals. As you might have guessed by the name, myoglobin is related to hemoglobin, which you probably have heard of. Either ways, I highly recommend reading more about these proteins as they are fairly interesting. Unfortunately, we almost certainly go into as much detail here.
The other manner in which they are used, and that you are probably more familiar with, is as a culinary term. Now, red meat is a meat that starts off red when raw and becomes a darker color as it is cooked. This is in contrast to white meat, which starts off as a pale color and maintains a pale color as it is cooked. The terms red meat and white meat are used to refer to different meats from mammals and fowl (birds). As such, you will not hear these terms applied to fish or other creatures. This mostly holds for culinary uses. In nutritional science, the term white meat can be applied to non-dark meat coming from fish and fowl (excluding the legs and thighs of fowl, although, this also holds for culinary uses of the term).