At some point, at some level, you really do need to just learn what a dot product is and what a matrix is. It's not weird notation or jargon, these are fundamental concepts.

Just like if you want to really learn how programs work you can't refuse any explanation that talks about "variables" or "functions" because that's jargon.

You can explain it, but it's going to be more at the level of "the network looks at the words" type explanation.