Well here's an explanation of what klippa is, taken from a few years of in depth learning of Chassidus:
Consider a situation where someone is having a good period in their life. Things are going great, they're succeeding in all sorts of areas, when suddenly there occurs (ch"v) a tragedy in this person's family. The situation, so to speak, "covers" over his regular joy, not allowing it to shine through as usual.
Another scenario: consider someone who is extremely intelligent, but has a speach impairment which effectively prevents his great intellect to be expressed outwards properly.
In Chassidus/Kabbalah, oftentimes the words Darkness and Light are mentioned. In a (very) general sense, these terms can be observable in the above instances. Light = where things are looking good, you can see a bright future ahead, etc; intellect, where ideas are clear in your head, the answers are known to you (like when you turn on the lights in a dark room) and so on.
Darkness = the hidden state of those things, like (from the above examples) a speech impairment or a tragedy.
The thing is, that darkness isn't really a "thing". All it is, is a lack of light. But I cannot, for example, make a device that creates darkness.
In Chassidic teachings, G-dliness (meaning, a positive spiritual expression, whether as a miracle, as a positive state of being, or quite simply a palpable, practical connection to G-d) is likewise represented by the term "Light".
And then there's the darkness which blocks off the G-dliness, something which can occur in many different ways. One classic example: when the world is in full-on "G-dliness" mode, it is clear and plain for all to see that all is in the hands or G-d, that He is running the show, and so on. So when something (or someone) claims proudly (whether by word of mouth, or by its very existence) that it exists independent of G-d's will, this is a sort of "covering over" the light of G-d shining through, so to speak.
Or, in a more extreme fashion, when there exists a situation or a case of anything which negates the Torah (and thereby G-d/G-dliness), this is a form of darkness, or--you guessed it!--klipa.
Much like a "klipa" (a shell/external covering) covers over a fruit and protects it, so too klipa in the spiritual sense covers over the contents hidden beneath it.
The fact that we call it klipa and not darkness is a topic on its own--part of it has to do with what I mentioned above, that darkness has no real essense about it.
Let me know if you want further details.
I'll just add one more important anecdote:
There are two types of "klippa". One is referred to as "klipat noga", and the other "shalosh klippot tmei'ot".
When I get home, perhaps, I'll expound, since I'm writing on my phone and it can get rather tiresome!