The word "ringer" has at least three contexts or meanings in golf:
A ringer board or ringer report shows the best score each player has posted during a set time period for each hole on a specific course and set of tees. Your group could have a gross ringer board, net ringer board or both. The gross ringer board would display the best gross score for each hole, whereas the net ringer board would show the best net score on each hole.
The ringer tournament, sometimes called an "eclectic" tournament, is one in which the best score posted on each hole by a player during multiple rounds is added up for one 18-hole score total for each player. An alternative way to look at this type of tournament is that it is an individual "best ball" tournament in which the best ball on each hole is selected from the players' multiple rounds.
We've all heard of someone bringing in a "ringer" for their foursome. It refers to a really good golfer often with the implication that s/he has entered an event under false pretenses.
Below is a sample of one player's scores with the first best score on each hole highlighted from our Handicap System. Under the scores is a one-row listing of the best scores. A ringer board or ringer report would be a compilation of this one row for all players in your golf group.
Below is a sample ringer board for a fictional eight players sorted by lowest 18-hole total first.