I have come know of Huffman and Arithmatic encoding that try to curtail redundant data and thus compress data. Why are they called Entropy encoding? What does that mean? Why not just call them compression encoding?
The term entropy comes from the field of information theory. Information theory posits that unexpected messages bear more information than expected ones. For instance, saying that there will be a solar eclipse tomorrow has much more information (assuming it's true) than saying the sun will rise tomorrow. Saying the sun will rise tomorrow, while true (and important!), has very little information for most recipients because they have pretty much 100% expectation of it.
Anyway, you can prove mathematically that information is maximized when all of the possible messages have equal probability. This maximizes the randomness or "entropy".
A perfect, lossless compression scheme could theoretically reduce the number of bits of a message to $ceil(log_2(entropy))$ but no further. Lossy compression schemes can reduce further, but information will be lost.
I personally am not fond of the term "entropy" because I associate it more with the 2nd law of thermodynamics. I believe that that association was intentional though, in the sense that entropy (in the thermodynamics sense) implies randomness and chaos, while low entropy implies orderliness.