Imperial federation is when a bunch of different places that are owned by the same country work together more officially. So, imagine you have a big toy box with lots of different toys in it. Maybe you have a doll, a teddy bear, some puzzles, and a few cars. These toys are all part of the same toy box, just like how different places like Canada, Australia, and India are all part of the same country, the British Empire.
Now, let's say you want to play a game where all the toys work together to build something really cool, like a tower made out of blocks. To do this, you need to get all the toys to work together and follow some simple rules. This is kind of like how the British Empire wanted to make all its different colonies work together more closely and follow the same laws and rules.
In the case of the British Empire, this would mean giving more power to a central government located in Britain and having representatives from each colony sit on a big council to make decisions. It could also mean having more trade between the different colonies and making sure they all followed the same laws and customs.
So, just like how you need to work together with your toys to build something cool, the British Empire wanted to work together with its colonies to make something bigger and stronger. This idea of imperial federation was talked about a lot in the late 1800s and early 1900s, but it never really happened because some of the colonies didn't like the idea of giving up their own power to a central government.