Intercessory prayer is just a big term that describes the very simple concept of praying for someone else. There are two ways to look at it though – (1) you praying for others and (2) the flip side of asking others to pray for you.
We pray for others at every Mass, but it’s also an outstanding practice to establish in your home. This can be done very simply by just keeping a list of people (“God, please bless Dad and Mom, my godparents, grandparents, our priest, the pope”, etc.), but can be done at a deeper level by keeping a list of prayer needs. Praying for specific things like Grandma’s surgery, safe travel for Dad, or the baby to sleep well tonight goes a long way in the art of developing empathy for others, and it allows us to watch for concrete answers to our prayers.
Working on the other side of this prayer “coin” is asking others to pray for us and, as Catholics, we know that this list of “others” includes not only people we see every day, but also angels, saints, and our loved ones who have gone before us. All of them are likely face-to-face with God and are happy to present our needs to Him!
Parents, I’d also like to mention that if you want to see progress in your relationship with your child (especially one in the 4th grade and up range), every now and then ask him or her to pray for you. Something like, “I think I’m going to have a hard day at work today. Can you pray for me?” shows that you think he’s mature enough to enter into adult things, show that you trust him, and shows that your faith is something you talk about. It helps your child to start to picture himself in a more grown-up way, and that is certainly one of your goals!