I could understand something like "the quality of being intricate and compounded".
When I was a student, my parents insisted on daily update of lessons (whatever taught has to be revised on the same day). They believed it could reduce complexity regarding my studies. I never cared this in my teenage, as I had plenty of romantic dreams(like most boys). And I never executed the above plan! I remember my mother's nervous colleague who had a number of wallets for keeping money for different purposes. We all are afraid of Complexity!? We find out a variety of methods for handling it. But sometimes I feel that Complexity is worthy (That is a different story). Some people are much bothered about this complexity and the implications of it ..At last they take asylum of spirituality (Where they say they can find Brahma-The ultimate knowledge). I don't do Share/Forex Trading because it I find it complex. My mom found Mathematics/Physics very Complex. Some say Theory of relativity is Complex. Thus complexity has different facets.
A surgeon, a civil engineer and a software engineer were chatting at a bar. The discussion rolled around to whose profession was the oldest. The surgeon said that his was, since in the book of Genesis, God created Eve from one of Adam's ribs, and surely that involved surgery. The civil engineer countered by saying that before God created man, he created the heavens and the Earth from chaos, surely a feat of civil engineering. The software engineer just smiled and said "Where do you think the chaos came from?"
That one was a well known joke! (Chaos is state of disorder; It is pronounced like 'Ke-yos')
http://pespmc1.vub.ac.be/COMPLEXI.html(Try this and let me know whether it was useful).
I feel, complexity is a characteristic 'God'? has filled while creating the world. He filled Abstraction also here-see my previous posts. And things are as we see/experience today because of complexity. Is complexity just residing inside mind, or it is there in the universe. I believe it is not just a feeling but some thing filled in nature. I believe so because of my exposure to ' Dialectical materialism'. This is becoming too informal...! Let me stop here. My friend is waiting as we planned to go for a movie. I 'll try to have a more authentic post on Complexity and reorganise(edit) this post. I am in a hurry as he is waiting.