The Demarcation Problem

Philosophers call the problem of separating science from non-science “the demarcation problem.” Let’s start by asking the following question:

(1) Why is the demarcation problem important?

In other words, why should we bother trying to come up with criteria for separating science from non-science?

Then we can attempt to ask the question:

(2) What is the best solution to the demarcation problem?

In other words, what exactly is the difference between science and other forms of enquiry?