Symmetric bilinear form is a way to measure how similar two things are to each other. It's like trying to figure out how much two shapes match up with each other.
Imagine you have a line with two points on it. A symmetric bilinear form would be a way to measure how close together or far apart those points are.
It's called "symmetric" because if you swap the two points around, you get the same answer. It's also called "bilinear" because it involves two things (in this case, the two points on the line).
Basically, a symmetric bilinear form is a way to compare two things in a way that's fair and makes sense. It can be used in lots of different situations, not just lines and points!