Differences In Wireless Standards
This is simple way too broad a question. However, a couple of points could be made. 

A primary improvement in LTE is the use of OFDM as the modulation scheme. This improves signal quality by mitigating frequency selective fading effects. 

LTE also proposes a more improved architecture (eNodeBs etc.) which define an Internet based scheme. All voice and data traffic are routed on the Internet i.e. using the IP protocol!

A layman answer to why LTE produces greater data rates is simply owing to the above two reasons, higher bandwidth (more spectrum) and efficient spectrum sharing schemes.  

I also want to add that the book Fundamentals of Wireless Communications by Tse and Viswanath treats the subject primarily at the physical layer, and you might want to read other books that look at this topic from a higher layer perspective as well. I would also suggest the website www.radio-electronics.com. They've got some simple explanations to the questions you have.