Learn French: L'orage a éclaté il y a deux heures pendant que je dormais. - The storm broke out two hours ago while I was sleeping.

This is the classic "interruption" rule you are learning! Je dormais (I was sleeping) sets the scene as the ongoing background action, so it takes the imparfait. L'orage a éclaté (The storm broke out) is the sudden, completed event that happened in the middle of that background, so it takes the passé composé.

Doesn't il y a mean "there is"? Why does it mean "ago" here?

You are right that il y a usually means "there is" or "there are." However, when you put il y a right before a length of time, it means "ago." Therefore, il y a deux heures translates perfectly to "two hours ago."

Why do we need que after pendant? Can't we just say pendant je dormais?

You have to use pendant que (while) because it connects to a full clause with a subject and a verb (je dormais). If you only want to use a noun, you drop the que and just use pendant (during). For example, you would say pendant l'orage (during the storm) but pendant que je dormais (while I was sleeping).

What is the infinitive of a éclaté and how else is it used?