the signal (or sign) for a meaning is not logically related to its meaning. In other words, the sound for cat does not sound like a cat or represent an actual cat in any logical way.
(The opposite to arbitrary is iconic—signs which DO bear relationships to their meaning. An iconic (or non-arbitrary) sign for a cat might be to call it a meow (thus, making it an example of onomatopoeia)).
messages can be both sent and received by the same individual. Not all animals can both send and receive messages (example, the silkworm's mating chemical).
the property of language to require only a relatively small part of the behavior of the speaker and to be context-dependent. In other words, we can talk about this class while driving to the mall! (But, then, dogs can bark and chase squirrels at the same time, too!)
not all aspects of language are innate. For example, a child raised in China will speak Chinese, but his or her sister, raised in America, will speak English. Certain bird songs and chimpanzee signals also seem to be learned. However, a dog's bark sounds the same regardless of country raised in.