So, this bliki thang is running on a reserved Amazon EC2 t2.micro instance. The only part of that link that isn't explained by the link is "reserved". Reserved instances are basically paying the bulk price for server minutes: you commit to a year or three of uptime, pay up front, and get a pretty big discount. So, basically, you get a server on the internet for not much money, and it'll never crash (where "never" means "99.999% chance of it never happening", if I can be sloppy with probability).
Looks like you can update all software via aptitude. Keystrokes: U (uppercase), followed by g.
(Don't know if this handles kernel updates.)