a share of stock

     A share of stock is actually so easy to understand as to make the level of confusion surrounding it suspicious--as in perhaps it IS all a diabolical plot. That said, a share of stock is a part interest in the corporation that issued the stock. If a publicly owned (stock-issuing) corporation issues on million shares of stock, and you buy one of them, you have purchased a millionth part of the corporation. You are a part owner--one part in every million of that corporation is yours.
     The stock in publicly owned corporations (remember that means stock issuing, not government owned) usually comes with a vote--one vote per share of stock. It's not exactly a democracy, which would have one vote per person--it's just how a corporation is run. Stockholders elect the board of directors of the corporation. The board of directors is headed by a chairperson of the board, or a chief executive officer (CEO).
     If you own stock through mutual funds, you have probably given your vote as a "proxy vote" to an employee of the mutual fund ( a mutual fund buys and sells shares of stock, and then sells shares in itself to investors--much like "holding company" of the 1920's, now illegal).