Okay, so imagine you have two groups of people - one group is called Anglo people and the other group is called Irish people. They have some different ways of doing things and some different beliefs.
But sometimes, some people can come from both groups! These people are called Anglo-Irish people. They might have an Anglo name like “Smith” or a Irish name like “O’Brien” but they are a mix of both.
In history, these kinds of people had a lot of different experiences. Sometimes they were accepted by both groups, but other times they weren’t. And sometimes they had a lot of power and sometimes they didn’t.
So being Anglo-Irish means you come from both the Anglo and Irish groups and you might have had some different experiences because of that.