There are two kinds of contrast the review might be talking about. Despite sharing a name, they're really two different concepts (isn't language awesome?). They both might be related to aperture, though, so without context, it's hard to guess which.

The first is micro contrast, which is explained in detail at What is "micro contrast" and how is it different from regular contrast?. In short, this is more closely related to the perception of sharpness than to the overall impression of tones, and lenses vary in this way due to the optical formula used and quality of materials.

A lens can also affect the overall contrast, by introducing veiling glare. You can read a bit about that as part of my answer to What characteristics make a good lens good?, and some related concepts at Is it possible for a lens to produce too much contrast? The basic concept here is that stray light bouncing around in the lens raises the lowest black level to a shade of gray, reducing the overall range of tones between that level and pure white. So, a lens with a lot of veiling glare will have reduced overall contrast.

Both of these can be affected by aperture — see the note about veiling glare at What impact on image resolution does the aperture have?, and some technical detail about micro contrast here: For MTF, why does 10 represent contrast while 30 represent resolution? (note that the different colors on an MTF chart typically represent different apertures).