Meaning of "medium write error" when burning a CD

I have been burning music onto CDs, using my Apple iMac desktop and Apple external CD burner/player unit for many years. I know I can burn 1 hr 19 mins onto my blank CDs so I never exceed that time. I only use highly regarded CD brands and over the years I have burned hundreds of CDs. Now when I go to burn a CD I receive the error message "Attempt to burn a CD failed. The burn failed because of a medium write error". I can see where this problem has been raised in the past but the only suggestion was to try a different brand of CD. As I said, I have been using Kodak and TDK CD for years but this problem has only arisen in past few months. No matter how many songs I attempt to burn, same result. I have used different CDs from different packs of blank disc, I have altered number of songs and therefore running time etc, same result. I even purchased a new Apple CD burner/player unit, same result. Both units will play all CDs, both professional and my home burnt discs, but will not burn a complete playlist, no matter how many songs I have on the playlist. 

Can someone please help me with a translation as to what this error message refers to. I spoke to Apple Care yesterday, the operative hadn't heard of the error message and could not assist. I presume it is some sort of software problem but I have not done anything to change my setup or procedure. Thank you Denis