Here's a breakdown:
* J'ai = I have
* les cheveux = the hair
* courts = short
* et = and
* bruns = brown
You can also say:
* J'ai des cheveux courts et bruns. (pronounced: "zhay day shuh-voh koor eh brun") This is a more casual way to say it.
* Mes cheveux sont courts et bruns. (pronounced: "may shuh-voh son koor eh brun") This is a more formal way to say it.
All three phrases are correct and convey the same meaning.