When someone you know is going through a difficult situation, you can ask other people to pray for them or think about them. The kinds of situations that you might ask people to "keep (someone) in their thoughts and prayers" for include:

• Someone at your church had a family member pass away.
• One of your cousins is having surgery.
• Your good friend's house burned down.

You can write or say any of the following:

Keep them in your prayers. 

Keep them in your thoughts.

Keep them in your thoughts and prayers.

"Thoughts" is a good choice if you're not religious, or if you're writing to others who aren't religious.

This is formal expression. People usually ask this in written English or when speaking to large groups of people.