A share is a special piece of paper, similar to a bank note. Because it is valuable, it is also called a security. If you own a share, you own a share in a company. That is why shares are also called share certificates. Shares can be bought and sold. Trading in shares usually takes place on the stock exchange. Nowadays, of course, this trading is done mainly by computer and no longer with paper.
Something similar to shares already existed in the Middle Ages. The very first share is a document from 1288 that certifies partial ownership of a copper mine in Sweden. In the 19th century, the share system spread very quickly because people wanted to use it to pay for the construction of railways. Since that time, there have also been fixed laws for share trading.