A corporation is a company that is owned by stockholders. A publicly-traded corporation, like Facebook, Inc., is a company where shares of stock (small quantities of ownership in the corporation) are traded in a public stock market.
If you look at the current quote for Facebook and it tells you that the share price is $131.88 USD, it means that you can purchase one share of stock for $131.88. If you do, you will be a part-owner in Facebook. There are roughly 2.40 Billion shares of Facebook stock out there, so for every share you hold, you own about 0.0000000417% of the company.
The shares of stock are bought and sold at a stock market, where brokers representing stockholders trade shares of stock in every public company. To buy or sell shares of stock, you need to open an account with a stock broker.
The price for a share of stock changes continuously, and is based on supply and demand for the stock. The up arrow that you saw means that the current price Google was showing you is higher than the price was at the end of the previous day.
To earn a profit trading stock, you need to sell shares of stock for a higher price than you bought them for.