A business man puts his reputation on the line when he promises a client that his product will be of X quality at T time. It's a completely different thing than if he merely said in passing that he thinks it will be X good. When a person promises it means they are assuring you that you can hold them to their word on this matter.
It's the same sort of thing with personal relationships, too. It's not exactly 'reputation' on the line, but no one would want to put their friend off being their friend because they aren't reliable to their word.
And so this social practice has helped people make many good stable agreements over the years. You could say, it's helped make relying on people more reliable! If you say you'll do something and you forget, then it's not clear how blameworthy you are. Perhaps you're careless, or perhaps it was a simple mistake. But if you promise someone you'll do something and forget, this is more obviously very neglectful of you and therefore blameworthy. After all, everyone knows the rules of promises.They're serious stuff, you can't just neglect to remember.
But if promises are so great, why don't we use them even more?! Why don't I get my friend S, who's always 5 minutes late, to promise to be on time, and this way he has to make the extra effort that he's not currently making or else he might lose me as a friend? Why not order promises at every single junction?
Well, quite obviously, we don't do that because that'd be horrible. Specifically, it would be horrible because we need to, to get along with each other, be a bit more tolerant of each others mistakes. We also need to be tolerant in other ways that effect promises, like we need to be tolerant that people change their minds. So the question really is, what makes the instances where it's good to make a promise so special that we are less tolerant of our friends making a mistake (like forgetting, or not being able to do it) or having the freedom to change their minds?
The intuitive answer is: when the promisee really needs the promiser to keep their promise. It's a bit annoying that S is always five minuets late, but it's a fairly tolerable quirk as far as quirks go, particularly in an age of smart phones. But if a person is injured at the side of a road, and you promise to come back for them with help, forgetting isn't really OK. Or if a dad promises his son he'll be at his birthday party, it wouldn't really be OK to change his mind in preference of the pub. But wait, now we're in the territory of things you're probably obligated to do regardless of the promising.
So the criteria needs to be that the action is not something you are obligated to do unless you promise to do it, and yet something that you could fairly be not tolerated for not doing. Perhaps our answer lies where we started, with the business man trying to keep your business.
Here's an example: Rebecca asks John, her friend, if he can be around tomorrow night because she needs to go over a very important pitch she'll be giving at work that could get her a promotion. He promises he will. If he didn't keep this promise, unless he had a very good reason, he wouldn't be a very good person to be friends with. This is actually completely different from my friend S always being 5 mins late, because this kind of thing won't really effect how good a friend that person is (we'll assume the friendship has other assets).
certain relationships come along with certain things you actually have to be reliable for in order for that relationship to last. Good neighbours have to water the plants when you're on holiday and keep the noise down after 10 PM. Friends have to be there for you when you're having a personal problem. Boyfriends and girlfriends have to share an affection. But these are consensual 'have tos' I am using. Without your continued agreement you don't have to be a good neighbour or a friend, or a boyfriend/girlfriend, or a two people trading, or anything other kind of human relationship. Promises are one of many ways we confirm we want to keep 'doing business together', so to speak, and accept the cost of doing so.