Ok, here are the links:

* When a firm decides whether to take on new projects, they look at the projected profit of that project, and compare to their cost of capital. Only projects whose profit exceeds the cost of capital should be executed.

* Stock prices influences a firm's cost of capital, eg when raising more money.

* Relative stock prices also influence, in mergers, say, who takes over whom.

* Via all these levers and more, stock prices help select which projects of all possible ventures are realised, and who manages them.

* All of this is aimed at funding those projects that produce the highest output relative to the resources dedicated to them.

* All of this only works if stock prices are a somewhat accurate reflection of the prospects of a firm; in other words, if the share price reflects the fundamental value of the firm.

* Short sellers (and long buyers) that analyse firms and trade when they perceive a discrepancy between share price and fundamental value can trade upon that insight, which will have two effects: a) it will tend to bring the share price closer to the fundamental value, and b) it will be profitable for the firms that are correct in their assessment.

That's basically the big picture story.

There’s a better answer in this thread, but a tl;dr/eli5, is that if all I can do is buy a stock then the only information available in the price are the people who believe in the stock/bond (usually as a proxy for belief in the company). This means that all the people who believe the stock/bond is no good have no way to lend their belief to the price of the stock/bond. This represents an optimistic asymmetry in the stock/bond price. By having the ability to short, some of the asymmetry is removed thus making the price better able to reflect the future expected value of stock/bond. That’s what makes it “more efficient”.