If you want a chance at big returns, you have to be willing to take on big risk. It's as simple as that. High interest savings accounts represent one of the lowest-risk "investments" out there, and accordingly they offer one of the lowest returns on investment. People typically use high interest savings accounts for an emergency fund, a place to "park" their money after taking it out of the stock market during uncertain times, a place to save up for a future purchase, and/or as the "cash" portion of their retirement portfolios.
There are plenty of professionals who can help you tailor an investment profile that best suits your particular needs. As a starting point, you can go to your bank and ask to speak with someone about investing. They'll ask you questions to get a handle on how much risk you're willing to take on, then they'll make recommendations on how to invest your money. You should keep in mind that the bank will of course try to sell you their own investment products, so shop around before making a commitment.