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Laurie Voss wrote No, Claude's watermark doesn't make the writing worse which is probably the most accessible starting point. If visuals help, Laurie pointed to this interactive watermarking post.

The idea and research behind the watermarking solution being proposed by Anthropic is SynthID Text which huggingface introduces here with code examples for getting started with it.

This post from Anthropic does a good job of explaining the whole thing in a nutshell in this paragraph. The core gist being that while probabilities or odds of what is generated are unchanged, this doesn't impact the model's weights, but rather "randomness decider" uses an internally-known key rather than an RNG.

Watermarking uses low-stakes choices like these—which occur many times over a piece of generated text—to leave a pattern in Claude’s responses. That pattern is undetectable to the reader, but is detectable to anyone who has a key that encodes it. When watermarking is used, choices are still made at random, but the source of the randomness is different. Instead of using an arbitrary random number generator to pick the next word, watermarking uses the key and a few words that come before to settle what word the model should pick. That is, the words that Claude picks are still random, but now, one can check the sequence of words and see if it’s consistent with the choices Claude would make if it was using the key. If it is, one can assign a probability that the text was generated by Claude.