First, the Enchanted creature gets +1/+1 for each +1/+1 counter on other creatures you control. This is for each counter, not just each creature. Plus, it gives the creature vigilance and the ability to pay 1 White mana and tap to Bolster 1. Because it's an instant speed ability, it can be used at the end of an opponent's turn.
The best use for this card, sadly, would be in a Heroic deck, which lost everything when Theros block left Standard in October 2015. However, Gleam of Authority did sneak into an Azorius (White/Blue) Heroic deck at GP Kyoto in April 2015. That being said, there were creatures that can amass +1/+1 counters still in Standard for some time. These included very playable cards such as Servant of the Scale, Anafenza, Kin Tree Spirit, Avatar of the Resolute, and Managorger Hydra, among others.
But, wow, this card is awesome in a Heroic deck with all of the +1/+1 counters that deck produces. Hero of Iroas makes this card cost only a single White mana to cast. Plus, it even gives you another way to Bolster. This card just seemed too good to not ever see play, but it just never got much of a chance without Heroic around in Standard. Even though there were enough +1/+1 counters running around for this to do something mean, it never really caught on.
However, Gleam of Authority does still see play in a few EDH decks, particularly with the Commanders Anafenza, the Foremost and Daghatar the Adamant. It's definitely a decent card in those particular decks.