Information theory has been important for the statistical analysis of languages, and especially for cryptography. Shannon's precisely defined entropy allows you to measure how many possible decodings there could be for a message. If you are designing a program to encrypt secret messages, you want to get more entropy, since that means anyone who wanted to break the encryption would have to work through that many more possible messages. Researchers have tried to apply information theory in many other fields. Other researchers are using the tools of information theory to measure the capacity of nerve tissue.
Newer evidence suggests that DNA has built-in error correcting protocols.
Work remains to be done in this area. Aging might be understood as a breakdown in DNA's ability to carry information along, an increase in noise as our bodies fall into physical entropy. If you're really bold, you could even come up with a new way of looking at the universe, where existence lies on a foundation of information, instead of matter and energy. The entropy of thermodynamics involves decay. If you assume that the universe is a closed system, the whole thing is sliding further into entropy every time anything happens.