Being poor in spirit is, essentially, recognizing one's dependence on God and turning to Him in true humility - knowing that He provides not what we deserve but what He desires to give as a reward for our effort. "Perfection" is defined as being "complete, whole, fully developed". Therefore, being "imperfect" means being "incomplete, part, partially developed" - being, to some degree, an unfinished, "natural (wo)man". This leads to an interesting meaning of repentance that is radically different than what was taught in ancient Israel (the Law of Moses perspective), with its emphasis on works.
The "classic" definition of repentance can be summarized in the following way: "feel sorry for your mistakes and stop making them". It is, in a very real way, a process of surgery - attempting to cut out and discard the "bad" from within us, so that we will stop making mistakes. This can be incredibly destructive for three reasons: first, it can confuse "sin" (things we choose to do, knowing we should not) with "transgression" (mistakes or violations of a law that are not intentional actions) - which means that people can spend enormous time and energy beating themselves up about and trying to rid themselves of weaknesses that often are beyond their control without outside help - things that have been paid for already by the Atonement; second, it assumes that we are competent surgeons (which deserves an entire thread all by itself); and third, it takes one's focus away from the powerful nature of true repentance (the changing of one's mind and view which changes one's very nature) - a process that is outlined clearly in the life and words of Jesus.
I need to step back at this point and emphasize a critical point: Repentance IS a process of change that involves ridding ourselves of those tendencies that keep us from being Christ-like. It DOES include gaining control over those things that cause our transgressions. However, it does NOT need to be a guilt-inducing, depression-causing, overwhelming chore. That happens when repentance is viewed as the companion to the type of perfection that I described previously - when repentance comes to mean eliminating mistakes and walking completely in lock-step with a detailed list of do's and dont's without ever stumbling. Let me emphasize again that "repentance" means changing one's VIEW about God, oneself and the world. It means SEEING the process differently - I would argue in the empowering way taught by Jesus Himself in the Sermon on the Mount.
To illustrate what I mean, consider again that the admonition in Matthew 5:48 to be perfect means to be whole, complete and fully developed, but also consider that it comes at the end of a chapter that lists specific attributes and actions - and the admonition itself begins with the word "therefore". What does this mean? It means "because of what has come before" - or "through what has come before". In that light, Matthew 5:48 says:
"Be ye (through what I have said so far) complete, whole, fully developed, even as your Father which is in heaven is complete, whole, fully developed."
This changes the entire meaning of repentance - since it says that reconciling to God is a process of acquiring the characteristics listed by Jesus as leading to perfection - adding them to your character - NOT cutting out pieces of yourself and assuming the holes will be filled somehow. It means repentance is the process of closing the gap between what we are naturally (incomplete, part, partially developed) and what He has commanded us to become (complete, whole, fully developed). It is a process of addition (becoming more) - not subtraction (becoming less). It is a process of acquisition, not elimination.
Think of a bucket full of liquid that is, to some degree, impure. The goal is to make the liquid in the bucket pure. You could attempt to do so by identifying the impurities and trying to remove them with just the use of your hands while not removing the pure liquid - or you could allow an expert chemist to add pure liquid to your bucket that would isolate the impurities and force them to spill from the bucket - replaced by the liquid that was added. Each is an effort to change the composition within the bucket, but the first is destined to produce frustration and heartache, while the other heals and fills and never depletes.
[FireTag made a comment (12/3/11) that I really like, and I am inserting it here to add clarity and meaning to the post:
"The analogy of the chemist struck me as a little odd. Adding liquid would DILUTE the impurity, not remove it. Would this be like those who try to do more and more good works to cover up the impurity within, yet never deal with the faults at all?
A chemist would use some process that did separate the purity from the impurity. So is seeing ourselves differently an inherently impurity separating process?"]
To make this practical:
If you struggle with a temper that manifests itself through yelling at your kids, you can try to "overcome" this tendency in one of two ways. You can take the classic approach and exert tremendous effort to recognize when you are about to lose it and, in that moment, exert even more effort to control that tendency by suppressing it - assuming that if you suppress it often enough you will gain total control over it. The problem is that the temper has not been eliminated; it simply has been suppressed, which means it still is there. When that effort to suppress fails and the temper flares again, you feel like a failure, since your effort couldn't stop the outburst.
On the other hand, with a different VIEW, you can look more deeply than just at the manifestation (your temper) and focus on the cure (becoming poor in spirit) in ALL aspects of your life. You can focus on the character trait that Jesus has identified as part of becoming perfect (in this case, poor in spirit) and allow Him to help you rid yourself of the underlying cause of the action. You repent by giving Him your burden (a temper) and agreeing to carry his yoke instead (walking humbly with Him). You repent by giving Him your heart and letting Him change your actions. You repent by forgetting about what you want to do and accepting what He wants you to do. You repent by ceasing to try to lessen who you are (eliminate part of yourself) and allowing Him to increase who you are (adding perfecting characteristics). In short, you repent by "losing (your view of) yourself" and "finding (His view of) yourself".
This changing of your view probably will not be immediate, but it is worth any effort. For myself, I have chosen to tackle this process in a very simple but systematic way (described here), but each person needs to take the first steps in whatever way makes sense individually.