I have been looking at this service and I cannot figure out the business model. It would seem that myibay is providing a free service with no method to profit from it. What is in this for myibay? I assume this not a charity.

It's based on two sources of income:

1. Selling a Windows based software (works as an interface for myibay service with some extra features to make auction management more easy).
http://www.myibay.com/download/

2. Donations.
http://www.myibay.com/login/donate

Please note that both of them are optional and not required for general usage.
The service itself is free. Some simple add-ons (like Firefox add-on, Opera button etc) are free as well.

You always get an unlimited number of snipes no matter how you support it (supporting by sending "thank you" or posting a short review somewhere are good ways too).