Nonhuman persons are entities which are not Homo sapiens but still qualify as a person. In common parlance, the words "human" and "person" are used interchangeably, because, for the most part, every human being is a person, and there don't appear to be any nonhuman persons in existence. However, I think that there are four different categories of entities that are not humans, but are still people. All four categories don't appear to exist, but seem possible.
Although the Hominina ancestors and cousins of Homo sapiens, which includes over a dozen species in the genus Homo and the various Australopithecina, are now all extinct, many of them showed signs of complex tool making and reuse, the creation of jewelry and paintings, a mastery of fire, and even the burial of their dead. This high degree of intelligence suggests that, even though they were not Homo sapiens, they still all fit the definition of "people."
While there is no credible evidence of life on other planets, let alone intelligent life, there doesn't appear to be anything special about the formation of life on Earth that would prevent it form springing up on other planets as well (a process called abiogenesis). If we were to meet an extraterrestrial life form, and it were sufficiently intelligent, it would be proper to call it a person even though it is clearly not a human.
Computer scientists have only been working on artificial intelligence (AI) for a couple decades, but already they have created some very impressive programs. Currently, AIs can be designed to perform pretty much any task a human can do, only vastly better. However, nobody has been able to create an AI that can even pass a Turing test, let alone demonstrate consciousness. Nonetheless, scientists keep churning out better AIs all the time, and, since there doesn't appear to be anything supernatural about the human brain, an artificial consciousness should be possible. If that happens, the AI will not only be a nonhuman person, but will also become the first nonliving person.
Complex consciousness appears to have only evolved a single time on Earth in our human ancestors. Some anthropologists argue that the more intelligent animals like chimpanzees and dolphins have a limited consciousness, but it is not to the level of humans. However, there doesn't appear to be anything to prevent a species that currently doesn't have consciousness from evolving into one that does. Given our current understanding of genetics and our propensity for breeding, humans may one day even create a nonhuman with consciousness. Evolved animals are essentially the same as intelligent alien life, only they would have formed on Earth based on the terrestrial foundations of life (DNA, eukaryote cells, etc.) rather than a totally alien foundation of life.