Sharing an interest

How do shares work? It's probably something everybody should know - especially as a lot of superannuation money these days is invested in shares (so I hear). But what makes a piece of paper either more or less valuable - and if there is no intrinsic value in the scrip itself - how does a sliding share price throw fear into the hearts of investors? And if I have shares in a company - and haven't checked the price for a while (since shares are a long-term investment?) why would the headline "Predators moving on as (insert name here) shares slide" pique my interest - especially given my lack of understanding of how the whole share-scene works - although, to be fair, I do understand the general supply/demand concept.