This rule is one of the most difficult in French (even French people have trouble with it!).

The past participle agrees with the direct object when it is located before avoir auxiliary.

Subject	Direct Object before avoir	avoir in the present	Past participle
Nous	les	avons	envoyés	hier.
Je	l' (=la)	ai	apprise	par coeur.

Some examples:

• J'ai envoyé les lettres hier. Je les ai envoyées hier.
  I sent the letters yesterday. I sent them yesterday.
• Pierre a pris la voiture pour aller au ski. Pierre l'a prise.
  Pierre took the car to go skiing. He took it.
• Elle a vérifié les résultats trois fois. Elle les a vérifiés trois fois.
  She checked the results three times. She checked them three times.