What do these red and blue icons mean in Adobe Premiere?
The blue icon on the clips means your clip has a proxy file attached to it, and the red icon means the proxy file is missing from that clip.
Proxies are lower quality versions of your video clips that you can generate using Premiere and Media Encoder. The advantage of using them is that when you are using very large video files, Premiere can become slower and less responsive. When you generate smaller proxy files, Premiere uses those instead if you click the "Use Proxies" button in the transport controls:
If you can't see the "Use Proxies" button, you might need to click on the plus icon in the transport window to edit which buttons are visible:
There's a good tutorial explaining how and when to use them here:
and Adobe's page is here: