The only background given for Man-At-Arms in He-Man and the Power Sword is that his people were "Masters of all weapons." He seems to be well known in this version of Eternia, but little information beyond this is given.
On page 8 of this story, there is a mysterious figure on top of one of Castle Grayskull's turrets, who is only identified as 'another warrior' and then on page 9 the text simply states that "Skeletor and his accomplice failed to notice the other warrior departing through the shadows in his heavily armed chariot". Reading between the lines, the warrior would appear to be Man-At-Arms, who later appears at He-Man's home riding the Battle Chariot and seeking help in the fight against Skeletor. However, this is never confirmed.
For the second wave of minicomics, Man-At-Arms is first referred to as Teela's father. the minicomic The Tale of Teela! reveals that years ago he saved the Goddess from having all her power drained by a magical clone created by Skeletor, and since the Goddess' duties impeded her from raising the now powerless clone, Man-At-Arms raised her as his own daughter and named her Teela.