How does a typeface "sparkle"?

There might be a few different things implied by this. Sometimes when people talk about a typeface ‘sparkling’ or ‘dazzling’ what they are actually referring to is phenomena in perception of text, which usually result from a particular typeface being used at an inappropriate size, but may also involve things like choice of paper or rendering environment on screen. I don’t think ‘sparkle’ is a singular phenomenon with one cause, but rather a collection of phenomena characterised by the perception of overall colour (texture) of the text as unsettled. So rather than perceiving an even texture within a narrow spatial frequency, the reader has a sense of shifting light and dark as he or she tries to focus. Fine hairlines and details rendered too small shift in and out of resolution during reading, because our eyes are constantly moving even during fixations. This requires extra effort, and makes reading tiring.

I almost always read foundry promotional text — including our own — as evidence of how difficult it is to describe a type design. Used in that context, I assume ‘sparkling’ in the sense of champagne, an associative cliché like ‘elegant’ or ‘lively’ that doesn’t really mean anything definite or specific but may suggest something generally positive to the reader’s imagination.

As an aside: the difficulty of describing a typeface in words suggests AI-generation of new typeface designs from text prompts is unlikely to be successful. I always have several ideas for new typefaces in my mind, and I can’t describe any of them in any way that would accurately convey the idea to another person or to a machine.