A stock certificate is a paper document indicating ownership of shares of stock in a corporation. When you purchase stock, your ownership is registered by the transfer agent and a stock certificate is mailed to you.
In modern times, most stockholders find it convenient to allow their broker to keep their stock certificates for them. There they are registered in street name. Then you rely on the broker to maintain accounting records for your shares and to mail you company reports, proxy statements, and related documents from the company. Most brokers use outside services to mail these documents. Mailings are often delayed somewhat, but most are timely.
Shareholders may still order out stock certificates after a stock purchase or from a brokerage account if desired. Some do this for safekeeping to keep their shares from being loaned to short sellers. The main reason might be to participate in a company's dividend reinvestment program.
Certificates must be safeguarded. Selling the stock requires signing the back of the certificate and delivering it within three days to your broker. A lost stock certificate can be replaced, but only with difficulty.
Fortunately stock certificates and their owners are registered. Unlike bearer bonds, stock certificates cannot be sold by anyone who finds one. Stolen stock certificates are not marketable.
Mutual funds also issue share certificates, but they are even more rare than stock certificates. Most are held by mutual fund companies.