This case is important because it set up the idea that the federal government can do more or less whatever it wants. It set up a broad definition of the power of Congress under the Constitution.
Before this case, it was not clear what Congress was allowed to do. There are very specific things that the Constitution explicitly says Congress may do. These are called expressed powers. But are these the only things Congress may do? This is the question McCulloch decided.
In this case, the Supreme Court ruled that the "elastic clause" is what we should pay attention to when deciding what Congress can do. It says Congress may do anything "necessary and proper" to carry out its expressed powers. In this case, the Court said that this clause allowed Congress to set up the Bank of the United States even though the Constitution never says "Congress may set up a bank."
So by ruling in this way, the Court said that Congress can do whatever it wants as long as that is not prohibited by the Constitution. Big difference, right -- Congress can do anything unless the Constitution prohibits it rather than Congress can do only what the Constitution explicitly says it may do.