What a share is
A share (or stock) is a small piece of a company. Owning one means owning a slice of its future profits, and its price moves with what people expect those to be.
A slice of a company
Big companies are split into millions of equal pieces called shares. Buy one Apple share and you own a tiny part of Apple: its factories, its brand, its future profits.
Why the price moves
A share's price is what buyers and sellers agree on right now, and it reflects what they expect the company to earn in the future. Good news pushes it up, bad news down, and fear or excitement can push it further than the news deserves.
Two ways to earn
You earn when the price rises above what you paid, and when the company shares its profit with you as a dividend.