So, let’s take that out and we are back to old, classical vector algebra. It’s like a person with a bunch of sticks to figure out which one to lay where in a 2-D plane to separate one class of objects from another, provided class definitions are already known.
The problem is which particular shape and length must be chosen to show maximum contrast between classes.
We need to arrive at a function definition, in such a way that the value a given function takes changes drastically (e.g. from a large positive value to a large negative value).
SVM is often great for two-class classification problems, and different variants also work well for multi-class problems.