It seems that Mojang’s multiplayer sessions service are down for maintenance (source). You can check in here and we will post when these services are back up. Here are some important tips:
- You can’t do anything – it’s Mojang’s problem, and they claim they need help from Amazon to fix it.
- There is no estimate of when the services will return.
- The reason you see some people on servers is because they went on before the sessions stopped working. As long as they don’t leave (or there is a server reset), they can play.
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Also please not that you should not bug them about getting it back up, that will only annoy them, plausibly slow them down, and make it take longer to get back up.