Why is manufacturing an important industry?

Well, in simple terms you've got three main sectors of the economy. There's primary industry at the start of the chain, which includes miners, farmers, and anybody else who collects raw materials. Secondary industry encompasses manufacturing, and everybody else who takes those raw materials and processes them into something useful. At the other end of the chain is tertiary industry, which sells those products on to you and me in shops.

If manufacturing didn't take place, the primaries would have nobody to sell their raw materials to, while the tertiaries wouldn't have anything to stock the shelves in their shops.

Perhaps more importantly than any of this, if the secondary industry didn't exist, our houses would be empty, for nobody would have manufactured any of the things we use. And our houses wouldn't be here either, as nobody would have built them. And then we'd be right up a certain creek without a paddle.

Because nobody would have bothered to make a paddle.