CHE COS' (instead of CHE COSA) is a matter of elision, a common rule in Italian to make speech flow more smoothly. When a word ending in a vowel (cosa) is followed by a word starting with a vowel (è), the first vowel is dropped to avoid a "clash" between the two sounds: the final "a" in cosa is removed and replaced by an apostrophe. The result: instead of the clunky Che cosa è, it becomes the fluid "Che cos'è".
In modern Italian, you will often hear this shortened even further to simply "Cos'è?", which follows the same rule.