"Tocar" in this context means "to be the turn of". For example: Ahora le toca a Cristobal hablar sobre las nuevas instalaciones. Now it is Cristóbal's turn to talk about the new facilities. Le tocaba a María habla, pero no quiso. It was María's turn to talk, but she did not want to. Ahora, a mí me toca preguntar y a ti te toca responder. Now, it is my turn to ask questions, and your turn to answer them. As an extension of this meaning, you can use it as "it is someone's duty to do something". Yo ya hice lo que tenía que hacer, ahora te toca cumplir tu parte. I already did what I had to do, now it is your turn to do your part. I hope this helps.