Besides real estate much property can be put in Shares. They reperesent the ownership and investment in companies.
Shares can be on the name of a person. In that case a register can mention who are the shareholders.
In Belgium shares can also be on the name of the person who holds the paper which represents the share. They are called bearer shares. These are unnamed, unlisted shares. While the concept of bearer shares sounds good, there are some specific reasons why they should be avoided in the United States.
For shares of large corporations on the stock exchange the ownership can be represented by an electronic version of the share.
Very basically, corporations are fictitious legal entities owned by groups of investors, who each individual own equity interests called "shares" in their particular entity.
Investors pour capital into the corporation, and return shares of stock (representing their equity interests) in return. The investors are now shareholders. The shareholders elect directors and officers to run the corporation.