Lay ecclesial ministry is when grown-ups, like you and me, help out in church when they're not priests or nuns. These grown-ups are very important because they do things like teach classes, help out during Mass, and take care of the church. They work with the priest to make sure that everyone at church feels welcome and happy.
Sometimes, these grown-ups go to special classes to learn more about how to help others at church. These classes teach them how to be good leaders and how to talk about God in a way that everyone can understand.
So, imagine going to church and seeing lots of different people helping out, not just the priest. That's what lay ecclesial ministry is all about!