Natural creatures are those creatures which occur naturally within the Prime's landscape and which are neither from the Feywild like eladrin, the Shadowfell like shadar-kai, the Elemental Chaos like fire giants, nor the Astral Sea like devils. This includes such creatures as deer but also larger or more powerful creatures like dire wolves or dinosaurs. Many of Toril's humanoid inhabitants are also natural creatures.
Oddly, some creatures which do have an extraplanar origin are considered "natural." These include tieflings, who are descendants of breeding between humans and fiends. Similarly, some creatures exist in other planes but are considered "natural" such as githyanki. Exactly what makes a creature "natural" or not seems to depend on bloodlines then rather than actual location, since drow, which originated on Toril, are considered fey rather than natural creatures. Similarly, githyanki, in spite of having originated in the Astral Sea, are the descendants of humans transformed by illithid enslavery and tieflings, in spite of their outsider heritage, are primarily human in blood.
Since outsiders are determined as being composed of extraplanar essence, it is likely that the natural world itself has an essence of its own, from which natural creatures are primarily composed.
All natural cratures breathe, eat, sleep, live, and die of natural causes, with the exception of undead, who are already dead and therefore can neither die nor live, do not breathe, do not sleep, and in most cases do not eat. Except for the undead, however, this generalization hold strue.