I have occasionally heard the terms method overloading and method overriding used interchangeably. While the difference between these two concepts can be relatively easily explained, the ...

Use Java's extends keyword to derive a child class from a parent class, invoke parent class constructors and methods, override methods, and more.

I'm getting better with Java, even to the point where I'm almost comfortable with it, but the purpose behind one concept still eludes me: What is method overriding, and why should I care about it?