Ensure you are downloading the Online PDF proof to your computer and open in Acrobat Reader.
See: How to view an Online PDF proof
During the proofing process, your artwork will be flattened to avoid any press issues. Flattening transparency means creating opaque areas that look transparent - these opaque areas have to fit together like a mosaic, each piece right next to the next. The result is that sometimes white gaps between these slices show (even though there is no white space between the slices). In the vast majority of cases, this appears only on screen.
These are usually caused by:
Transparencies
Pantone colours
Large images
The best way to check if these are preview errors or an actual print problem is: zoom in and out!
If the white lines change position or disappear at some point, then they are just screen artifacts and you can ignore them. If they stay at the same position and get thicker when you zoom in, then they will most likely print and you should upload a new file converted to CMYK and without transparencies.