Online communities, which have become an integral part of the day-to-day life of people and organizations, exhibit much diversity in both size and activity level; some communities grow to a massive scale and thrive, whereas others remain small, and even wither. In spite of the important role of these proliferating communities, there is limited empirical evidence that identifies the dominant factors underlying their dynamics. Using data collected from seven large online platforms, we observe a universal relationship between online community size and its activity: First, three distinct activity regimes exist, one of low-activity and two of high-activity. Further, we find a sharp activity phase transition at a critical community size that marks the shift between the first and the second regime. Essentially, it is around this critical size that sustainable interactive communities emerge. Finally, above a higher characteristic size, community activity reaches and remains at a constant and high level to form the third regime. We propose that the sharp activity phase transition and the regime structure stem from the branching property of online interactions. Branching results in the emergence of multiplicative growth of the interactions above certain community sizes.