The guide directory included in the package has 8 published scripts that contain dozens of examples in tutorial style. The resulting HTML files are also installed in the Help Browser under the "Chebfun Toolbox" heading.
I've not tried this out, nor tested it yet. That will take some time. But what I've seen suggests this will be interesting and potentially useful. A lot of effort has been invested here in these tools.
The only thing I'd have liked to see is a published set of demos, with more explanation around how to use it and what the demos are showing. There is a directory (chebtests) of some tests of the tools, but they have virtually no comments in them. Derek has a good suggestion, to read the paper by Trefethen. Here are a few links of interest:
The papers shown are quite readable. I'd highly recommend them.
My only source of dissatisfaction here is with a lack of examples. These files need extensive demos and DOCUMENTED examples that explain how to use them for the person who might be interested in using them. The fact is, it does not look like that would be difficult to do, and I'd welcome that addition.
My gut says these tools are worth a 5 star rating, IF you know how to use them and what they do. Without a good set of clearly documented examples, my gut wants to rate them as only 4 stars.