As stated by what appears to be the founder (or a key person) in this thread in the bitcointalk forums, calling himself senbonzakura: "profit from the bank must be halal (permissible). So if the bank lends at interest, the interest then is profit for the bank, and that would mean muslims(or jews/christians) cannot buy shares in the company as the bank deals with interest, which makes it non-permissible/haram."
The motivation for running the IBB seems to be somewhat charitable, with this (edited) comment from the same person: "The problem that those 3 religions is trying to solve is human greed. Under that philosophy it does rightly condemn interest, for the reason that interest places the 'haves' infront of the 'have nots'.... From a humanitarian-philosophical perspective [the IBB] makes perfect sense, from a capitalist perspective it doesn't".
However, it is being run as a business. The IBB website says it's listed on the GLBSE, and it has asset, revenue, and dividend figures. The website doesn't go into much detail about what the bank does, but if you were to read the above linked forum thread you'd probably learn a lot more about it. Since the bank is paying out dividends, I doubt that those purchasing stock in IBB are doing it purely as a donation.
So, to summarise:
- The IBB is profit based, but doesn't earn money from interest.
- If you assume their revenue chart is accurate, it earns money
- Their revenue stream includes (complete list so far): Shares/Dividends, Arbitrage, Gratuity
- Even though IBB doesn't charge interest, they accept donations from borrowers. Depending on the culture of the customers, this could be considered to be like making optional interest payments.