Six-star hash is hash described as the top grade in a commonly used melt-rating system. Producers often pair it with “full melt” to signal material that melts readily with very little solid residue. The rating is an industry convention, not a regulated certification.
It doesn't mean six times stronger, a particular THC percentage or six rounds of filtration. It isn't a rosin grade either: Lowtemp's bubble hash and rosin comparison applies melt grades to bubble hash and dry sift and says rosin isn't graded on melt.
Who gave it the stars?
That's the first useful question. Producers, retailers and reviewers may use different conditions and different thresholds, and even the scale isn't settled. Lowtemp's version runs from cooking grade (1 or 2 stars) to half melt (3 or 4 stars) and then straight to full melt (6 stars). Five stars doesn't appear on it. A scale with a missing step is loosely defined, and nothing on that page makes it a universal standard.
If a shop advertises six star, ask whether that's the producer's batch designation and which product format it refers to. A retail menu can shrink a detailed label to a few words and lose the context on the way.

What six star doesn't establish
A micron range describes screen size, not a guaranteed grade. Pale color doesn't prove careful separation, and a photograph can't measure melt behavior. Aroma can be memorable without establishing the absence of contaminants.
The number isn't a promise of a particular effect either. Potency needs batch-specific labeling, and subjective effects vary. Reading the label helps keep these kinds of information apart.
Is it worth paying more?
That depends on the actual product, what you want and how clearly the claim is supported. If you're specifically after full-melt hash, the grade matters to your decision. If you want an easy-to-handle rosin badder, you're answering a different question.
A high star rating doesn't mean a product suits every device. Check the maker's directions for both the product and the hardware. The full-melt versus rosin comparison explains the format difference, and hash grades covers the rest of the scale.