A stock market to be alive, needs regular visitors who buy sell stocks daily. An individual may not have that many transactions to do daily.
Also if all stock holders and willing buyers start coming to a place daily to buy/sell (Trade) stocks of many companies, it may become a mess.
Setting up a stock exchange involves many costs. You need money to operate. There is a need for revenue model.
Keeping all these in mind, stock exchanges offer memberships and only members are allowed to trade in stocks of that stock exchange.
These members pay regular fees to stock exchanges.
These members are also called as stock brokers, if they offer their services to buy or sell shares you want to.
They will charge you a fee for the same.

