Yes they absolutely do. Maybe we forget cd burners for home use because we have phones, the cloud or even thumbdrives nowadays.
But many businesses, universities, schools and other institutions still use CDs a lot - therefore the burners!
These institutions use cd burners and cds to keep information stored on their files. For example, many places all over the world have students submit their final essays on university in a cd disc so they can keep the essay on the student's file for some years.
Many governments also accept cds when delivering information regarding lawsuits, tax return and much more...as thumdrives could bring the risk of setting up viruses and such.
Also video games and music cds are still sold all over the world, so cd burners are needed for that.
So to answer your question yes, CDs are still used and cd burners are necessary for that too!