A few thoughts:
1. In Greek, the word is ταπείνωσις, which means "lowness or low estate in life," as in, one who is vulgar (not noble or landed or educated or refined), not well respected, having no position of authority, no money, no fame, and none of the good things that mark a person of greatness, success, or divine blessing. That's the literal meaning. Metaphorically, this sort of "low estate" is often applied to one's moral or spiritual reality, so that one can be a spiritual zero, "leading one to perceive and lament his (moral) littleness and guilt," as Kittle puts in in the TDNT
2. The Theotokos, in Luke 1:48, says "For He has regarded the lowly state (ταπείνωσις) of His maidservant; For behold, henceforth all generations will call me blessed." In other words, the humble condition, in that she had no social standing, is unworthy of such a great calling, etc.
3. There is a famous Icon from Holy Week, Η Άκρα Ταπείνωσις, The Extreme Humility, which depicts a thoroughly humiliated or abased Christ. That is the "icon" of true humility: One who is actually truly blessed willingly suffering the insults and persecution of those who say he is not blessed.
4. Martyrdom and bearing insults aside, in many writings of the Fathers, humility means (a) never thinking you are spiritually great, no matter how much fasting, prayer, almsgiving, etc. you do; and (b) never making a show of your asceticism. Thus, the holier a saint becomes, the more she is thoroughly convinced that she is the worst of sinners. If you ever think you are more spiritual or holier or better than someone else, no matter how "bad" they are, then you are full of pride, not humility. And, of course, if you make a big deal to others about your ascetical practices, then you're totally missing the point.
As Jesus said in Matthew 6, "But when you do a charitable deed, do not let your left hand know what your right hand is doing, that your charitable deed may be in secret; and your Father who sees in secret will Himself reward you openly...But you, when you pray, go into your room, and when you have shut your door, pray to your Father who is in the secret place; and your Father who sees in secret will reward you openly...But you, when you fast, anoint your head and wash your face, so that you do not appear to men to be fasting, but to your Father who is in the secret place; and your Father who sees in secret will reward you openly."
That's why Archimandrite Sophronios wrote that "truly charismatic people do not make a show of their gifts and graces."