elaborate how and what part?
In general principle, Islamic banks follow what's known as Fiqh al-muamalat ie. the Islamic rules on transactions. They share profits and loss's rather than Interest, you have to be very well read on Shariah Law's to interpret the rules for modern Islamic Economics.
A very basic example of how this works is that, if you opt out for a mortgage from an Islamic Bank, the Bank will "buy" the property for you and sell it to you at a certain mark-up or margin (be it profit or loss), and you can keep paying the installments to the Bank at the agreed agreement price of the house at the time of the contract.
@RB
there was a reason I asked for a "specific" query, like how the the mortgage system works, how agreements, joint-ventures, safe-keepings or Islamic Insurance etc. works, that would make it easier to answer a question, the way you asked made basically means to explain the whole system :D, which I fully don't understand myself, all in all it is a very young and interesting field and makes a good read as-well.
