I've just read the NASA news item From Pedicures to the Peregrine Rocket, Paraffin Wax Proves Its Worth.
The project started when researchers at Stanford discovered that paraffin fuel burns three times faster than conventional fuels, and therefore can provide more thrust and higher performance than existing hybrid rockets. They approached Ames for assistance in measuring the burn rate at larger scales and to contribute to the maturation of the technology.
I think the "three times faster" means that a given volume (or mass) of the solid wax propellant in a given shape could be consumed in one third the time of a conventional solid propellant for hybrid engines, and so that factor of three speaks directly to thrust-to-weight ratio of the engine.
I'm not sure what conventional is, but I'm guessing it's one of the synthetic "rubbers" like HTPB.
Why would wax burn roughly three times faster than other fuels? And why the sudden interest now — is there some specific technical challenge that has been potentially solved allowing for greater thrust/weight, or is there a need for a low temperature robust hybrid rocket on Mars (see below and in link) and the factor of three is a secondary benefit?
The paraffin-based fuel also works under challenging environmental conditions, like the very low temperatures found on the surface of Mars. The Mars Ascent Vehicle, currently under development by NASA’s Jet Propulsion Laboratory, aims to use the paraffin technology to return a sample from the surface of the planet to an orbiting spacecraft.
An nice summary of hybrid fuel combinations was linked in this insightful answer, and some of the links in Does the NK-33 engine require subcooled kerosene so cold that it turns to wax? helps one appreciate that one can think of wax as being more like solid kerosene than it is like rubber.