To have been more wealthy or in better condition in former times.
When it was first coined this phrase referred to people who had fallen on hard times, having previously been wealthy. More recently, the phrase is more often used to describe objects which are worn-out than people who are impoverished.
The line is first recorded in the play Sir Thomas More, 1590:
“Hauing seene better dayes, now know the lack Of glorie that once rearde eche high-fed back.”