I was about to add a snarky "Easy answer: Read the HN F.A.Q. level comment but after a bit of looking around the answer isn't obvious (yet somehow I sort of knew it through being a HN user) and using the Search box didn't return anything useful so instead of snark I used a bit of google-fu & here's your answer. HTH.
https://news.ycombinator.com/item?id=2456602
https://news.ycombinator.com/item?id=3848762
TLDR; Green Accounts are for users who are under 5 days old. You can see all their submissions at - http://news.ycombinator.com/noobstories
[Edit to add, Or perhaps it is 14 days as per https://news.ycombinator.com/item?id=3848820]
Double Edit: Confirmed, 14 days (not 5). See https://github.com/minimaxir/hacker-news-undocumented for a full list
New users have a green username. This is so you can provide friendly, helpful, notes to those users.
It marks new accounts (I think created in the last 14 days)