We do not have visibility into Facebook's ad approval process, so we cannot give information with 100% certainty why individual ads may have been disapproved.
Most common reason: Too much text in the picture
The most common reason why ads are disapproved is that the pictures have too much text. Facebook allows a maximum of 20% text of the image's area. Use the overlay tool to check whether your image has more than 20% of the area filled with text.
Update: Facebook has updated the process about the 20% rule. They do not disapprove the ads anymore but limit or stop the delivery of the ads. Read more here: Facebook Help article & use Facebook's Text Overlay Tool to assess whether Facebook will determine how much text is in your ad image and whether Facebook will let that image be delivered to your full audience.
Facebook's ads guidelines
Another reason for rejection may be that ads conflict with Facebook's ads guidelines. For example, advertising alcohol has restrictions based on country.
When there are issues with the links in the ads, you can use Facebook's Share debugger to check if there are any obvious errors in the links.
If you feel an ad should have been approved but was not, it is advisable to be in touch with Facebook directly. For more instructions, see Facebook's help article on rejected ads.