Today I started receiving a ton of requests to moderate comments on my blog, but when I looked at the comments they are clearly from multiple other people's blogs. What could be the cause of this and what do I do about this?
Those are pingback or trackbacks. They are mechanisms by which blogs alert each other about cross-linking or references to other posts.
Pingbacks and trackbacks are common from SPAM or scrapper sites so you do want to take a look and make sure you are not approving comments from disreputable sources but in general, these are normal and can be useful.
The pingback/trackback functionality has been built into WordPress for as long as I can remember. Your site probably sends similar "comments" to other blogs.