What is a Language?

What is it for?

A language is a means to convey and communicate ideas.
(A means is a 'tool').

How does it do it?

A language is essentially a self-contained system of signs ( or symbols).

http://www.bartleby.com/65/se/semiotic.html
The Columbia Encyclopedia, Sixth Edition. 2001.

What is a symbol in the context of a language?

A symbol is an arbitrary and agreed upon (conventional) representation that holds shared meaning.

Symbols are letters, marks, sound, etc.

For Example:

If I say or write 'potato',
you know what I am talking about.

Not because the word 'potato' looks or sounds like a real potato,
but because you and I have agreed (and have been taught)
that the word 'potato' will represent a real potato.

In Summary

A language is a fantastic tool that enables you and I to communicate, to discuss, to think, to debate, to plan, to do all sorts of things with ideas. As we manipulate ideas, we can transform our attitudes, actions, and lives.