This is aliasing, often called a moire pattern when it occurs against something regular, as in this case.

In this particular case, the actual picture is made of lots of little dots of ink in a regular pattern. Your camera sensor is also lots of little sample points on a regular pattern. When the spacing of the two are close (or multiples are close) but not the same, you get this moire pattern or beat frequency.

Scanning ink-printed halftone pictures is tricky. The best way is to scan at such a high resolution that there are a reasonable number of pixels per ink dot. Or put another way, use enough resolution to resolve each ink dot separately. Then you can digitally filter the image down to a more manageable resolution. Proper digital filtering will cause the ink dots to be averaged out from the initial high res samples, not just re-sampled at a lower resolution.

Think of a black and white ink halftone picture. You scan at high resolution, so you can see the individual ink dots in the scan, and how big each one is. In theory, all the pixels should be either full black or full white. In fact, it often helps to amplify the range about some midpoint to get mostly black and white pixels, since that's what the print actually has. At a fine detail as your scan, the print is either white where there is not ink, or black where there is ink. This may take 1200 DPI or more to obtain without noticeable moire pattern.

Now you can shrink this image to whatever resolution you really wanted, like 300 DPI for example. The digital filtering and shrinking process will take a bunch of original pixels into account to get each output pixels. This allows the output pixels to be shades of gray.