From the Super Mario Wiki
Rings is a Gymnastics Event that appears exclusively in the Nintendo 3DS version of Mario & Sonic at the London 2012 Olympic Games. The aim of the event is to score points by performing moves on the rings, with the winner being the one with the most points. The starting best record for this event is 16.600pt(s).
In the game's story mode, rings appears as part of the third challenge of Wild Ones Episode 2, Corner the Koopa King!, in which Vector must beat Bowser in it along with Weightlifting and Football. It also appears as the challenge of Wild Ones Bonus 1, Bowser's Blues, in which Bowser must beat Donkey Kong in the event. It also appears as the final part of the second challenge of Wild Ones Bonus 2, The Life of a Minion, in which Bowser must beat Vector in it and Javelin Throw, Double Trap, Football and Weightlifting.
In this event, the player performs a series of moves on the rings to score points, with the winner being the one who scored the most. Moves are performed by holding one of the A, B, Y or X buttons and the Circle Pad in a specified direction for a length of time to fill the meter. Depending on how full the meter is, the player will be ranked either bad, good, great or perfect, each awarding various different amounts of points, as well as bad for overfilling the meter. If the player fails to press the correct buttons in time, they will also be rated bad and not score any additional points. The player will perform four standard moves, and depending on their performance, either another standard move for a poor performance or a special move for a good one. A special move requires the player to hold down two of the A, B, Y and X buttons and the circle pad on a diagonal, and will award more points if performed well. If the player falls however, their character will completely fall off the rings before being given their final score.
1) Strength hold: Follow the displayed command and hold the Circle Pad and A/B/Y/X Button, then release.