Archival research is when you look at old stuff that has been saved to learn about what happened a long time ago. Imagine you are snooping around your grandpa's attic and you find a treasure chest with all of his old letters, pictures, and stuff from when he was a kid. By looking at all these things, you can learn a lot about what your grandpa was like when he was young and what things were different back then.
Archival research is when grown-ups do this same thing, but on a bigger level. They might go to a library, museum, or government building to look at old things that have been saved, like old letters from famous people, pictures of what a city looked like a long time ago, or important government documents. By looking at all of this old stuff, they can learn about what happened a long time ago and how things have changed over time. It's like time traveling without actually going anywhere!