One of the best definitions I heard is that integrity means saying what you'll do and doing what you say.
It's a quality that's actually quite hard to find: people say they'll call, or email, or pay, or turn up to a meeting ...
And what if they don't? Our clients and others notice the gap; they see how we behave with the little things; and then they make judgments about how we will operate with the big things. So the little stuff matters: they, too, need to be handled with integrity.