Q: What are these red circle symbols that suddenly appear in my iTunes library on my iPhone?

Just wanted to update in case anyone else was wondering what this was. It seems that despite my telling iTunes to copy all my music over, some songs were not. There is a "Download All" button (which thanks to the new iOS doesn't look like a button) I tapped and these songs were finally copied over. I don't understand why they weren't to begin with since they were on my phone this morning before the iOS7 update. Go figure?

Now I'm off to attempt reading my new iOS7 calendar. Anyone got a pair of magnifying glasses? Awful.

I found it at the top of the playlist on the right side, it's hard to find because it seems iOS7 buttons don't look like buttons anymore, just plain text links (my biggest gripe about this update).

Here's a cap from my iPad since my iPhone has already synced all my music and thus won't display any link. It's at the top of the list underneath the "Shuffle" link.

Just to note, the red circles with red squares appear to be a progress icon, displaying the progress of a song's download. My iPad library shows a cloud icon with an arrow instead, tapping it displays the red circle and the song begins to download.  My iPhone didn't show the cloud icon, just the red circle and tapping it didn't seem to do anything. My guess is there was a glitch displaying the wrong icon, tapping the "Download All" link at the top worked when tapping the individual circles did not.

Edit: I don't use iTunes Match anymore and turned off the service on all my devices. I quit using iTunes Match several weeks ago due to poor performance.

I wonder if it's iTunes Match (if you use the service) that's causing this problem. I quit using Match several weeks ago after it wouldn't work for a week. I called Apple who told me only 400 of my songs had been uploaded to the cloud, which wasn't correct because I had over 1500 songs in the cloud. After Match began to work again I downloaded all my music back to my devices and turned the service off because dumb me hadn't made a backup first.

Most of my music came from CDs as well but luckily had a net connection to update my database with the CD info. I've slowly re-added some albums over time to get rid of those pesky "Track 1" songs, basically rebuilding. I sorted my library by "date added" to make it easier. Match worked great... at first. After about a month it tanked, unable to connect to the iTunes store and updating my library across my devices. There are quite a few threads about this since the problem began. It began to work again after a couple weeks, but not 100%, still occasionally losing connection with the iTune Store. I ended up turning it off after I was able to connect and download all my music back to my laptop. I called Apple and they said my database only had around 400 songs, which was incorrect because I had well over 1500 I'd uploaded to Match. If I turned off Match then I'd have lost all that music. Here's one of the threads about our Match disaster.

https://discussions.apple.com/thread/5223301?start=0&tstart=0

Personally I wouldn't use it having had an awful experience (along with lots of other people). It wasn't an isolated problem and Apple never acknowledged it. I now make monthly backups to an external drive. Best of luck!