Certain animals gecticulate, babble and use very simple syntax to convey meaning. Primates, cetaceans, pinnepeds, elephants and birds seem to be the language champions of the animal kingdom.
Our cognitive abilities and the manouverability of our vocal tracts are, famously, second to none. We can say that human language is strongly informational, in the sense that it is open to interpretation. Most animal (and machine) languages are more like sets of preprogrammed instructions. Thus, a useful demarcation between animal and human language is the ability to rearrange words in order to convey new meaning. The more inflexible, whole sentences of animals are only weakly generative.