It means you are pretty or handsome apparently, but I was born on a Monday so it obviously doesn't necessarily follow :-)
I'm taking this wisdom from a well-known poem that goes like this:
Mondays child is fair of face
Tuesdays child is full of grace
Wednesdays child is full of woe
Thursdays child has far to go
Fridays child is loving and giving
Saturdays child works hard for a living
And the child that is born on the sabbath day is bonny and blithe and good and gay (note- gay meaning happy obviously!)
Actually,
it's strange how words have changed since that poem was written. Gay
has a whole new meaning now and bonny and blithe are never used today.
Bonny means attractive or beautiful and blithe means carefree in this
instance I believe.