In thermodynamics, entropy is the measure of disorder in a system.
Systems go from a state of low entropy, to a state of high entropy, as unusable energy increases.
In information theory, entropy is a measure of the number of bits necessary to transmit a message. A system with greater order can be described with fewer bits of information, whereas a system with greater disorder requires more bits of information to be described. This is fairly obvious when you think about it, and is the basis of how essentially all compression algorithms work, and is also a good way of determining if something is fairly random. If you cannot compress information easily, then it is probably more random than something which is compressed easily. This is because it contains more information, and thus cannot be summarized.