The phrase "rare public appearance" refers to a situation where an individual or group makes a rare showing in front of the general public. This could mean that they typically keep a low profile and avoid being seen in public, but on this particular occasion, they have chosen to make an exception and be seen by others. The word "public" here implies that it is not just a private event, but rather something that is open for anyone to attend or observe. Overall, the phrase suggests that the individual or group in question values their privacy and typically keeps a low profile, making this appearance all the more rare and special.