Humility is seeing yourself as God sees you - no more, no less (hence my frustration at people's pious attempts to be humble by degrading or ignoring their own talents, or by refusing to accept compliments). I believe it was St Augustine who said that if we saw each other as we truly are, we would be tempted to fall down and worship. So, all else accounted for, humility includes recognizing that we are awesomely gifted and incredibly blessed.
But it took me years to discover what I will call supernatural humility, which consists of allowing others to trample upon your dignity while holding fast to it inside. This is the humility displayed by the martyrs when they allowed their bodies, precious temples of the Holy Spirit that they were, to be mutilated and destroyed, and by Our Lord when countless calumnies were spoken against Him. They knew their worth was much greater than that, but were happy to suffer these injuries for the sake of our heavenly Father.
This kind of humility is a very practical virtue to work on in one's daily life. Ignore (or even smile at) that kid that ran into you in the supermarket rather than expressing your frustration at his careless disdain for your personal space. Work diligently at your tireless job without expectation of appreciation (also accept without complaint tasks far below your skill level). Quietly pick up and do the forgotten tasks for which other people in your household are responsible (sometimes).
These examples work best with strangers, though, and get tricky when they're with closer people. But building friendships I've found to be a different story. Between the command to love your neighbor as yourself and the analogy between spousal relationships and other friendships (analogous insofar as both are based in love of God), it seems clear to me that the telos (end) of every Christian friendship is to get your friend to heaven. So you want to enable them to persist in vice as little as possible without infringing upon the unconditionalness of your charity.
Scenario One: Road trip with one friend (read: little to no alone time for a full week). Both of us looking out for each others' interests so far above our own that we never stopped to consider whether what we thought the other wanted was really what they wanted. So communication fail, but also humility fail. What was needed from me was not to set aside my own legitimate needs and desires but to trust that my friend loved me enough to want to meet my legitimate needs and desires, and to express those so as to give them an opportunity to do so.
Scenario Two: Went out of my way to make plans with a friend for special quality time before I leave; other plans were then made for this friend over the plans they had with me, but this was not communicated with me until I asked about our plans. On an objective level, this was quite upsetting, but my initial response to this friend was not even one of disappointment; all I said was "good to know!" Sure, humility would just take the injury (which was my initial reaction), but friendship should not. Friendship required me to step up and demand a reschedule, not in the least because I know this friend had no desire to hurt me, and would benefit from the opportunity to develop the skill of being a little less oblivious to such things.
Scenario Three: My children slack off and don't do their chores. How much is it laudable for me to simply pick up after them quietly, and how much of that is simply spoiling them and enabling them to not learn to take care of themselves?
Humility is a tricky virtue, this supernatural kind none the less so. Like just about everything else that's good in this life, it's a balancing act. So the goal is to make sure I balance my humility with charity, not with insecurity. (Why are the worthwhile things always easier said than done?)