Sideburns were a variant of facial hair; they were thick patches of whiskers on the sides of one's head.
The Third and Fourth Doctor both wore sideburns (TV: Spearhead from Space [+]Robert Holmes, Doctor Who season 7 (BBC1, 1970)., TV: Planet of the Spiders [+]Robert Sloman, Doctor Who season 11 (BBC1, 1974).) - the Fourth's were red even though the hair on his head was dark brown. (PROSE: The Drosten's Curse) The Tenth Doctor described the Fourth Doctor as being all "scarf and sideburns". (AUDIO: Out of Time)
The Tenth Doctor was delighted to see he had grown sideburns after his regeneration. (TV: Born Again) He kept them to the end of his life, (TV: The End of Time [+]Russell T Davies, Doctor Who Christmas Special 2009 and New Year Special 2010 (BBC One, 2009-2010).) though he was once temporarily aged to a point he lost them, and later, all of his hair. (TV: The Sound of Drums [+]Russell T Davies, Doctor Who series 3 (BBC One, 2007)., Last of the Time Lords [+]Russell T Davies, Doctor Who series 3 (BBC One, 2007).) His fourteenth self, who was almost identical to his tenth, also had sideburns. (TV: The Power of the Doctor [+]Chris Chibnall, Doctor Who Centenary Special 2022 (BBC One, 2022)., COMIC: Liberation of the Daleks [+]Alan Barnes, DWM Comics (Panini Comics, 2022-2023).)