Investment is not the same as savings in the world of macroeconomics. If you are not purchasing a capital asset that is used to generate income, such as a machine, or with the expectation that it will appreciate in value, like a house, then you are saving, not investing.
You can save more than you invest, such as when a business purchases equipment with part of its profit and puts the rest of the profit in a savings account. On the other hand, you can actually invest more than you save. In fact, many people invest more than they save when they finance the purchase of a house, which is a capital asset.
It's possible to invest more than you have in savings because the savings of other people can be used to finance your own investments. A classic example of this is a simple savings account. When you deposit money into a savings account, you are making money available to the bank to lend to other people who want to invest. The bank pays you an interest rate for the use of your money, while it charges a higher interest to people seeking to use the money for investment.
You probably see a strong relationship between investment and savings at this point. Savings accounts provide the funds to make investments possible and determine the price paid for investing through borrowing. You can think of the price of borrowing as the interest rate you must pay on money borrowed.
If the supply of savings available for lending increases, the interest rate available will decrease, assuming all other factors remain the same. On the other hand, if the supply of savings available for lending decreases, interest rates will increase as borrowers compete for loans. Interest rates stabilize where demand for funds equals the supplies of funds.
