Non-U.S citizens cannot directly open an account with a U.S based broker as they would not possess the necessary documents, required to open an account with a U.S broker. But there are many U.S based international brokers like 'Interactive Brokers', etc, who allow users from multiple countries to open an account with them. Using that account you can easily gain access to the U.S markets.
A brokerage account is an account that facilitates all the transactions in securities. As you carry out monetary transactions through a bank account, buying and selling of stocks, bonds, commodities, etc can be done through a brokerage account.
Investors and traders need a brokerage account to execute their traders as well as to store the owned shares. Selecting a good broker is important as you will depend on them with your money. You could execute multiple things with your brokerage account. Some of them are mentioned here.
The partial answer is No. Most U.S brokers require certain documents like a U.S passport, Social Security Number, etc in order to verify your identity. This is a mandatory process and every user has to provide the necessary documents. Now unfortunately Non-U.S citizens would not have access to the necessary document due to which they will be ineligible to open an account.
On the other hand, many U.S brokers are international brokers and offer their services across the globe. Brokers like Charles Schwab, TD Ameritrade, Interactive Brokers operate on multiple exchanges across different countries therefore you can open an account with them to trade in U.S securities even if you are a Non-U.S citizen.