Okay, imagine that you really love someone, like your mommy or daddy, and you want to make them happy. One way you can do that is by praying for them, which means talking to God and asking Him to take care of them and make their lives better.
The apostleship of prayer is a group of people who all love God and want to make Him happy by praying for other people. They choose a special person or cause to pray for each month, and they all pray together for that person or cause. They also try to be good and loving people themselves, because they believe that by doing that, they are helping to make the world a better place and spreading God's love.
So basically, the apostleship of prayer is a group of people who try to be kind and loving to others and pray to God to help them. They believe that by doing this, they can make the world a happier and better place.