Learn Italian: Che cosa hai nelle borse? - What do you have in the bags?

It is a combination of the preposition in (in) and the feminine plural definite article le (the). Because borse (bags) is feminine plural, you use le, and in combined with le merges to become the articulated preposition nelle.

Why does the sentence use Che cosa instead of just Cosa to say what?

You can actually use either! Che cosa, cosa, and just che are all commonly used to mean what in questions. Che cosa is considered the most traditional and complete form, but Italians use all three interchangeably in everyday speech.

Why is there no word for you in this sentence?

In Italian, the verb ending tells us who is doing the action. The verb hai means you have (from the verb avere). Because hai is only ever used for the singular you, including the pronoun tu isn't necessary unless you want to add special emphasis.

How does the word borse show that there is more than one bag?

The singular word for bag is borsa. In Italian, most feminine nouns that end in -a in the singular change their ending to -e in the plural. This is why borsa changes to borse.