This Maxim seems to me to be about the way we interact as mortals. We are already told to “Keep yourself from insolence” by one of the other Maxims and this extends to other mortals as well as to the Gods. It is important to live together without boasting and drum-beating about who is ‘better’ than others – except where arête has been proven in the agon (struggle/contest). Even then, boasting is to be avoided as it can be a sign of hubris.
As mortals, we all have talents, but more importantly, we all have weaknesses. This Maxim is one that reminds us to live humbly because others are always going to be better than us in some area or another. I have been told that I am a good writer, but I can honestly say that, when it comes to physical things, others are better than I am.
When we follow this Maxim’s advice, society tends to run smoother because there are not people making claims they cannot back up and people tend to contribute their strengths to the greater whole. It is this contributing that makes a society as a whole great or not. When it works, it is a beautiful thing, but when people fail to live meekly within society then we begin to have problems with greed and other vices.