While the details and availability vary radically from institution to institution, some professors are given a certain budget to spend on whatever they deem appropriate (within limits).
In the United States, this is most commonly associated with more senior positions (e.g., endowed chairs). It is typically not a very large amount, but often enough to support some travel or undergraduate researchers.
In other countries, it may be structured differently. In particular, I have heard that some universities in the Middle East have been giving extremely attractive funding packages to professors as part of their program to attract foreign talent. My guess is that this may be the case with your professor, though it is impossible to know for certain without more information.