This Maxim is something that most of us could do well to look at. A person who makes a promise is obligated to do their utmost to keep it. As this is the case, we should be very careful what promises we make and to whom. We should even, or perhaps especially, keep promises to very small children so that they can learn the importance of those promises. We must ALWAYS keep promises made to the Gods.
But, this Maxim does not only say to be careful about our promises, but not to make them at all. This is similar to “Do not use an oath” and both Maxims convey much the same message to us. We are to be truthful at all times and so neither an oath nor a promise should be something that we should need to make except when we are called to testify in a legal matter, because once made the Gods want them to be inviolable. This is more than simply a matter of honor or ethics, but a matter of one’s personal integrity. Our integrity is one of the most valuable things we have, and in an ideal world would not be impinged upon. However, as this is not an ideal world, we have to actively keep it – and not making promises that we cannot fulfill is part of that.