There is not a distinct name for this style, but the style of these illustrations is endemic amongst vector illustrations. When a picture is rendered in pixels, it is called "raster". Raster images can get blurry or pixellated if you zoom in on them. Vector illustrations are different.Instead of defining the image by the location of colored pixels in a grid, it defines them through mathematically defined shapes. The result of this is that you can infinitely zoom on these, and never lose detail.
There are pros and cons to both mediums of image making. Vector illustration is common in advertising and graphic design fields because of the modularity of the designs. A vector design can be designed for a business card, and then relatively easily blown up and stuck on a billboard. That's an important quality if you're making a logo. Vector also has it's own set of limitations though, and that is part of why there is a distinctive "vector style". While vector images do not have to have this style, they often due to the natural limitations of the medium.