Okay, imagine you have two boxes of toy blocks, but they're arranged differently. One box might have all the blue blocks at the bottom, while the other has them scattered throughout. Even though they look different, they're kind of similar because they both have blue blocks.
Matrix consimilarity is like that, but with numbers instead of toy blocks. Sometimes, you might have two matrices (which are just boxes of numbers arranged in a grid) that look different, but they might still be kind of the same because they have some of the same numbers in the same places.
So people can use matrix consimilarity to compare matrices and see how similar they are. It's like they're trying to find the blue blocks that they have in common. If they find a lot of similarities, they might say the matrices are "con-similar" to each other.