Anglican-Roman Catholic dialogue is like when two big groups of people who have different ideas about how to worship God want to talk to each other and find ways to be friends. It's like when you meet a new friend at school and you have different favorite toys or games, but you still want to play together and have fun.
The Anglican church is a group of Christians who have their roots in England, and the Roman Catholic church is a group of Christians who have their roots in Rome. They have some different beliefs about how to worship God and what's important in their religious practices, but they still both believe in Jesus and want to be good people and help others.
So, sometimes, the leaders of these two big groups of people get together and have conversations to try to understand each other better and maybe find ways to work together more closely. They talk about things like how they read and understand the Bible, how they pray and worship, and how they try to make the world a better place. They try to find common ground and respect each other's differences.
It's important for these two groups to have these conversations because they both represent a lot of people around the world, and if they can work together, they can do more good things. It's like if two of your friends at school who you really like but who are very different from each other can work together on a really cool project, it can be even better than if they do it alone.