The main idea starts from the observation that noise (with a sense of randomness, lack of predictability) is hard to compress, while structured signals possess a certain amount of correlation that somehow can be compacted. However, it is interesting to take another perspective, which I borrow from Filtering Random Noise from Deterministic Signals via Data Compression, 1995, B. When one considers the original data as the "clean" reference, lossy compression adds a amount of loss related (generally vaguely increasing) to the compression ratio allowed.
Noise, at least divergence or loss from the original data, arises only with lossy compression. There are two main types: lossless compression, and lossy compression.
I will start the explanation from the compression viewpoint.
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