In form and function, language varies widely across space and throughout time. That being said, six key properties of language have been described by linguists. These six features are arbitrariness, cultural transmission, discreteness, displacement, duality, and productivity.
Arbitrariness of language is the fact that the symbols we use to communicate meaning to not have any natural form or meaning in and of themselves. For example, all of the words you are reading right now do not have a natural essence to them, but we have assigned these words to their particular meanings. The word table is not a table itself; rather, it is a word we have agreed means or signals for the idea of a table. Onomatopoeia differ somewhat in their arbitrariness, because these are words which replicate the sounds they describe. The word "plop" is intended to replicate the sound plop.
Language is both acquired by and continues the process of cultural transmission. Humans are not born with an innate understanding of communication in the way that birds or lions are. We must learn, along with other elements of culture, how to communicate with others using language.
Discreteness in language describes the fact that human language is composed of sets of distinct sounds. One sound on its own may convey one meaning, multiple sounds combined in a particular order convey a different meaning. Even repeated sounds have a particular meaning!
Displacement of language refers to the ability of human language to communicate throughout time and across space. In animals, language is primarily an exchange between stimulus and response — the meaning conveyed by animal language only works in context. When a dog barks, it is in response to whatever prompted the barking, and that bark can't really be used to express its meaning before or after the event. In human language, however, we are able to talk about things that happened a long time ago or have not yet happened. We might even read books produced hundreds of years ago and be able to make sense of them.
Duality describes the human ability to produce language in multiple forms. We can both write the word table and say it out loud, with both evoking the same idea of a table.
Productivity is a feature of human language which enables us to combine symbols (words, sounds, phrases) in new ways to express particular ideas. In my studies of the evolution of language, I heard an example that I think really expresses the nature of productivity. The form of language for our closest evolutionary cousin, the chimpanzee, is very fixed. Only one meaning can be conveyed at a time and it is in response to stimuli. If a chimpanzee were to come across a very tasty-looking bunch of bananas that were unfortunately on fire, instinct would determine how the chimp would call to its troop. The chimpanzee would either have to produce the call which implies food is available for eating, or the call to warn others of danger. The chimp might be able to create the "food" call immediately before or after the "danger" call, but they cannot combine them to express the idea that food is on fire. If we, as humans, came across the same flaming bunch of bananas, we would be using productive language in telling our friends that there are some flaming but otherwise tasty-looking bananas nearby.