From Destinypedia, the Destiny wiki
Rift is a Crucible match type introduced in The Taken King that later returned in Destiny 2 in The Witch Queen during Season of the Haunted in Iron Banner. It'll be added to the rotator in the upcoming 18th Season of Destiny 2.
Rift is an 6v6 objective-based capture-the-flag mode where Guardians need to capture a spark and deliver it into the enemy rift to score points. The spark has a shot-clock as well; if the runner does not get the spark into the enemy rift, they will be killed.
In Destiny 1, points are acquired the following ways:
Whereas in Destiny 2, points are acquired by only delivering the Spark to the enemy Rift.
The Spark spawn in near the middle of the map on a timer. Controlling the middle is imperative to success. Once the middle is secure, the Spark can be picked up and must then be carried to the enemies side of the map to their Rift. Players not carrying the Spark should lead the way, as the team without the Spark will spawn in near their Rift, often leading to a short full team battle. The Spark holder is the main target, as the points they would gain from dunking the Spark, and potentially killing all nearby players, is a massive boost. Shutting down enemy Spark holders as quickly as possible is highly important, as they closer they get to the Rift, the more points they will earn for their team. Ultimately, the game mode requires extreme team play in order to be successful, combined with smart map pathing to find a safe route to the Rift and shut down enemies.