There are several different forms of Islamic Banking. Specifically, in mudarabah you have 2 parties. One party, provides all the capital (rabb-ul-mal), other party provides management (mudarib). They split profits at a predetermined ratio.
In case of loss, only lender (rab-ul-mal) eats up the loss.
How is it different from non-Islamic banking?
In order to get capital, you take a loan and pay interest. Rab-ul-mal or the bank, never looses money.
In mudarabah, management or mudarib has a stake in the well being of the business because it gets a percentage of profits. This is not the case in loans.
In mudarabah, you don't pay an interest, instead your share of the profits is not 100%. This is similar to how venture capitalists invest in companies. They take a percentage stake of the company in return for capital. All management resides with the startup/mudarib.
why "Mudarabah" is not haram or not like Riba?
Why is it not haram? Bank/investor/rab-ul-mal has a chance to make money or loose money depending on how the company performs. If it is profitable, bank gets money. If company is not successful, it looses money.
In interest, regardless of how company performs, lenders always get paid first.