In context, the meaning seems to be "150 members". This seems the general consensus, and I can understand why. In the case of Humans, Earth will counts as one, Mars maybe (has been ever established if it's voting member?), and Alpha Centauri as another. If the case of Humans is typical, this would imply between 50 and 100 species. But you know, drawing conclusions from one data point is not a good idea in general.
Personally, I prefer to think that he meant 150 planets total, including colonies with a significant population and a degree of autonomy (but not necessarily full membership in the Federation). This would bring the number of species probably under 50, and probably much less. I prefer this figure because it would explain how the Federation can be kept in check by single-species political entities like the Klingon or the Romulan Empire. (Even if we imagine that it takes multiple single-species empire to keep in check the Federation, it's really hard to imagine that less than 10 species can be a threat to a huge federation of 150 species.) On the other hand, just like in real life, some species can be vastly more numerous and have vastly more resources than others, so the sheer number of members can be a meaningless metric.