"Low-profile" can mean several things. It can mean avoiding drawing attention, as in "Try to keep a low profile while you're in that part of town". It can also mean an object that is physically doesn't rise above the surface very much, as in a low-profile light or fan fixture, which stays as close as possible against the surface it's installed on.
There's an additional usage in racing, where low-profile means keeping a car body close to the track to improve aerodynamics; and often the term is used in multiple senses at once, as in "low profile body armor" -- it stays flat and close to the body, which makes it less apparent that you're wearing body armor under your clothes.
In the context of a camera grip, it most likely is referring to the physical shape of the grip, saying the grip is small and close to the camera body. I'm not familiar with what kind of camera we're talking about; low-profile in this context would, I suppose, be opposed to some kind of standard camera grip that's a big handle that sticks out and might get caught on objects in the environment. However, this may simply be marketing-speak, using language that suggests the grip is slim and unobtrusive even though, in reality, it's not significantly different from any other grip.
Without more context, it's hard to tell what was meant. Are you sure you quoted it correctly? "A low-profile grey and leather grip" doesn't make sense as a phrase. I would think it should be a "low-profile grey leather grip" (the grip is covered in grey leather and constructed to be low-profile). Alternatively, there could be a word missing between "grey" and "and" -- as in, "a low-profile grey plastic and leather grip", where the phrase plastic-and-leather forms a single adjective unit to describe the material composition of the thing.