Hi Wholey,
When you burn a CD from iTunes you can choose from three options: Audio CD, MP3 CD, or Data CD. Only the third option, Data CD, will preserve all the information about your music, but you're likely to have problems playing that in devices other than a computer. The second option, MP3 CD, will be playable on a wider range of devices, and should (I believe) preserve the info from tags like Artist, Album, etc -- though you may need to convert the tracks to MP3 in iTunes if they're in a format like m4a.
If you burn a regular audio CD, generally speaking, you're burning only the music itself, not the associated tags from iTunes. But there is a checkbox for "Use CD Text" in Burn Settings (the pop-up window that appears when you start the burning process) that, according to Apple, "disc players in some vehicles can display." So you might try this and see what happens.
There's a bit more detail here: iTunes 12 for Mac: Create your own CDs and DVDs
I hope this helps!