Banks built upon Islamic principles of profit, most obviously, make a profit through equity, which is the money value of property or an interest in a property. Investors share in profits and losses. Even if you lease a car through a regular bank, part of the calculation includes an interest rate. In the Islamic version of leasing, the interest payment is not an implicit part of the calculation. There is a rental payment for the object.
Islamic banks function in the U.S. mostly through leasing.
Also in other Arab countries there have been major Islamic bank transactions that basically lease airplanes to national airlines. Islamic banks in the United States and elsewhere attract depositors by offering opportunities for profit through leasing investments. Depositors buy a share in a portfolio of leases and get some proportion of the implicit profits.