Okay kiddo, so let's start with what we mean by "orthologous." Have you heard of the word "homologous" before? It means things that are similar because they have a common ancestor. So, orthologous things are a kind of homologous things, but specifically they come from different species and have the same function.
Now let's talk about a matrix. That's just a fancy way of saying a table of numbers. So, an orthologous matrix is a table of numbers that shows how similar the DNA or protein sequences are between different species for genes that have the same function.
For example, let's say we want to compare the gene that codes for a protein called insulin between humans and mice. We know that insulin is important for controlling blood sugar levels and that humans and mice both have insulin, so we can say that the human and mouse insulin genes are orthologous. If we compare the DNA sequences of these genes and make a table that shows how similar they are at each position in the sequence, that would be an orthologous matrix.
Scientists use orthologous matrices to study evolution and to try to figure out which genes are important for which functions across different species. It's like looking at a family tree and seeing which traits run in the family, but instead of people, we're looking at genes and different kinds of animals.