Learn French: Je lisais quand une branche est tombée.

This is a classic interrupted action sentence! Je lisais (I was reading) sets the background scene, which is an ongoing action in the past. The phrase est tombée (fell) is the sudden, specific event that interrupts that background. We use the Imparfait for the background and the Passé Composé for the interruption.

Why is the helping verb est instead of a for the verb tomber?

Most verbs use avoir in the Passé Composé, but tomber is one of the special motion verbs (often remembered with the Dr. & Mrs. Vandertramp list). These verbs always use être as their helper verb, which is why it is est tombée and not a tombé.

Why is there an extra e at the end of tombée?

Because tomber uses être as its helper verb, its past participle must match the gender and number of the subject doing the action. The subject here is une branche, which is feminine and singular. So, we add an -e to tombé to make it tombée.

What role does quand play here?