Avoir du pain sur la planche is a French expression that translates literally to “to have bread on the board” and means “to have a lot on your plate” and “to have a lot to do”.
avoir du pain sur la planche
to have a lot on your plate

Example sentences
This first example sentence uses the tricky verb rejoindre (to join), which I’ve covered thoroughly in this lesson.
Désolé, je ne peux pas te rejoindre ce soir. J’ai du pain sur la planche.
Sorry, I’d can’t join you this evening. I have a lot to do.
For this second sentence, il va falloir is the near future tense form of the commonly used impersonal expression il faut (it’s necessary).
J’aimerais bien passer le weekend chez vous, mais j’ai du pain sur la planche, il va falloir que je reste à la maison.
I’d love to spend the weekend at your place but I have a lot to do. I’m going to have to stay home.