First, and most obvious, if you have financial power of attorney, you are legally able to make investment decisions in someone else's account. The other person legally owns the assets of the account, but you are acting on their behalf. You are legally required to invest in a prudent way.
Can I buy stocks for someone else?
Stocks can be given to a recipient as a gift whereby the recipient benefits from any gains in the stock's price. Gifting stock from an existing brokerage account involves an electronic transfer of the shares to the recipients' brokerage account.