Stocks are ownership shares in a company. Anyone can buy a share in a public (ie available to the public, a simplified definition) company. For example owning 100 shares on issue of Company X out of 1000 total shares gives you a 10% ownership stake. You’re entitled to 10% of the dividends paid out of profits, and can vote at shareholder meetings etc.

A stock exchange is a market that matches buyers an sellers of company shares (“stock/s” and “shares” are generally used interchangeably). It facilitates transactions between different shareholders and stands in the middle of a buy and sell trade to effectively make it happen (now with technology backing these transactions to make it all run smoothly, again a simplified example).

At any given time there will be buyers and sellers of a stock at certain prices. For example if Company X stock last traded at $100, on the stock exchange there may be bids to buy at $99 and offers to sell at $101 - in order to transact on either side you need to “cross the spread”, which will move the price up or down by 1%. This is how stocks move. Smaller stocks generally have wider spreads, trade less, and therefore are more volatile than larger stocks.

Traditionally to access a stock exchange you needed a dedicated broker (a real person at a company) but now with technology virtually anyone can access the market cheaply and easily via online brokers, at least for individuals trading relatively small values vs institutional shareholders.