"Equities" is a needless complication when you can use the word "stocks". Fortunately, most people do say stock, or stocks. Equity refers to your ownership. If you've bought a few stocks in Facebook, you actually own a very small amount of it, even if Mark Zuckerburg doesn't call you for advice. That means you own some of the company's fortunes, for better or for worse. You might get paid a portion of its profit in the form of a dividend, or the company might spend its profits in order to grow.
The thing to remember is that stocks are pretty much always traded on the stock market. This means if you want to sell them, it is the market that decides what they're worth - not you. Stock prices can fall as well as rise. Don't like it? Blame the Dutch; they invented it.