What an interesting question!
This question is fairly complicated as true language is unique to human beings and as a result, is interpreted at both a scientific and cultural level.
If the desire is to describe human language, the key points are that it must communicate information with intent and purpose. (By this definition a parrot is not using language even when mimicking it).
It is also not purely repetitive and has a degree of human customization behind it. For example, the Voyager probe, now beyond the boundaries of our galaxy, is not actually using language even though it is broadcasting a set message. It is just repeating a series of sounds that happens to be meaningful in English but it is not language.
Each human language has it's own syntax, grammar, and structure. As long as a language has this, it is actually considered to be a true language (if the previous two points are also supported). For example, Klingon isn't a real language, but Trekkers have followed the rules of syntax and structure to make a new language that follow the principles of a language.
True language is also innate to human beings and it tends to spring up as a normal behavior developmentally, as children grow. This is unique to people as no other animal can spontaneously generate communication that isn't instinctive. When your dog barks, he is not using language although he is communicating.
True communication varies according to the needs of the person at the time. For example, there are differences in rate, volume, rhythm and meaning that are a part of true language. For example, the simple question "How are you?" can be interpreted many ways by the intention of the person saying it. It can be friendly, sarcastic, or even loving depending on the person's intent. This trait or ability is called a paraverbal communication and is unique to human beings.
Lastly, human language develops in four basic phases- babbling which is the repeating of non purposeful sounds. Next comes lallation which is the intentional repeating of certain sounds but not words (ta ta ba ba sa sa). The third aspect is echolalia speech which is simply repeating a word or sound without true meaning such as when a baby says "no" to everything without understanding. Lastly, before true language is telegraphic speech, sometimes called holophrase where small bits of language and syntax are expressed. (To most people this is what we call baby talk.) Example, "me go outside now". (Not a true sentence but we understand its meaning.)
I hope this helped you,