Scoring a try is the ultimate aim of the games Rugby League, and Rugby Union. Tries have the highest point value in the game, and most of the time if you score more than the opposing team, you will win the game.
Naturally, the team you're playing against are doing everything in their power to stop you scoring that try.
Actually scoring a try is in principle a simple thing. A player from the attacking team must place the ball with downward pressure in the in-goal area of the defending team. The player scoring doesn't need to be in this area themselves, they're perfectly entitled to stretch out and place the ball on or over the goal line with one hand if need be - only the ball needs to find the ground. The player also must be themselves in the field of play when the ball is grounded. If a player is trying to score in the corner, defenders will normally not try to stop their progress, but rather push them over the sideline before they can get the ball down. This can lead to some spectacular diving tackles, sometimes the difference between scoring and not being a matter of centimetres.
Point values for a try vary between the two codes of rugby. Rugby League awards four points for a try, while Rugby Union awards five. The higher point value for a try in union is needed to provide greater incentive to try to score tries - in this code, penalty and field goals are worth three points. A one point advantage for the extra effort required to score a try is not enough - it's easier, and possibly more productive, to work into position for a field goal, or keep possession of the ball in the hope of being awarded a penalty.
In Rugby League, there are a couple of additional rules in relation to tries - rarely used, but they're available for the referee if need be. The first of these, is the 'eight point try'. Once a player has scored a try, the defending team are not permitted to tackle, or attack that player in any way. It's legal to attempt a tackle to try to stop the player scoring, or to force them to ground the ball without running closer to the goalposts (important when determining where the conversion is taken from) - but once the try is scored, they're to be left alone. If a defender does do something like that after the try is scored, the referee may award an additional penalty, on top of the try. This means that a regular conversion is taken from the point it would be normally, but then a penalty kick for goal can be taken from directly in front of the posts. Hence the term 'eight point try' doesn't refer to an automatic eight points - rather the possibility of scoring that many.
Another rule that is sometimes used in Rugby League and Union is the penalty try rule. If a defending player fouls an attacking player, and in the referee's opinion that foul stops the attacker scoring a certain try, a penalty try may be awarded. The attacking team is awarded the try, and the conversion is taken from directly in front of the posts. The most famous Rugby League penalty try in recent years was decided the 1999 NRL Grand final, played between the St. George - Illawarra Dragons, and the Melbourne Storm. In the final minutes of the game, trailing 18-14, the Storm's Scott Hill took the ball mid air, in the Dragons in-goal area, off a bomb kicked by Brett Kimmorley. All he had to do was fall to the ground, and plant the ball to draw the game, with the chance of winning it if the difficult conversion was successful. However, a high tackle by the Dragons Jamie Ainscough knocked him unconscious, forcing him to drop the ball. After consulting the video referee, field referee Bill Harrigan awarded a penalty try, giving the Storm the conversion from in front of the posts. The conversion was successful, and the Melbourne Storm took out the Grand Final, in only their second season as part of the league.
Thanks to caknuck for letting me know that Rugby Union also has a penalty try rule. If I've made any mistakes re the Rugby Union's interpretation of this rule, please let me know.