What does "ASIC" mean? I stumbled on the terms "ASIC" and " ASIC Miner", what do they mean? Is this something related to special hardware?
ASIC or Application-specific integrated circuit is a type of circuit that has become very popular in the Bitcoin mining community. 

wikipedia defines it as 


  "An application-specific integrated circuit, or ASIC /ˈeɪsɪk/, is an integrated circuit (IC) customized for a particular use, rather than intended for general-purpose use."


Traditionally computer chips are made with variability of input in mind, meaning that a given chip should be able to do a wide range of things. Because Bitcoin miners only ever use their chips for Bitcoin mining, you can make chips that are really really fast if you make them solely with that purpose in mind.

This is how companies like butterfly labs can get such ridiculous speeds of up to 500 GH/s!