The Rift is cross dimensional portal which currently resides deep below the castle of Daemonheim. Not very much is known about the history of the rift, but it is known that the Mahjarrat Bilrach was searching for it for a long time. Bilrach may currently be digging through Daemonheim's depths in order to find it, however no one knows for sure.
According to Bilrach, the rift is a place where the barrier between the realms is weakened. He wants to make advantage of this in order to bring back Zamorak to Gielinor from the realm he currently resides in. Bilrach also uses the rift's weak barriers to unleash many fierce monsters, like the stalkers, behemoths and the Kal'Gerion demons, upon Gielinor. He uses those monsters to guard the dungeons he creates while digging towards the rift.
The strange power event which occured on the 23rd of January 2010 was previously believed to be caused by the rift. However, upon completion of the quest The Ritual of the Mahjarrat, a conversation with Ali the Wise reveals that the event was caused by the death of a Mahjarrat while under the influences of perfect planetary alignment, the same concept used in the rejuvenation ritual. This would imply that Bilrach may have died during the event and would explain how he did not attend the ritual, however since the end of the Fremennik Saga Nadir is not shown, it also could have been Lucien's daughter, Moia, who has been killed.
The strange power also attracted the Fremmenik's attention. They went to Daemonheim and are currently raiding the dungeons Bilrach created, trying to find the exact source of the power.
It is believed, and likely, that the many strange resources found in Daemonheim came through the rift from other dimensions.
The rift is also believed to cause various rooms below Daemonheim to replace themselves to another location, since Bilrach states in his journal that the rooms he digs collapse and reappear elsewhere. This causes much trouble for both Bilrach and the Fremmeniks seeking to reach the bottom of Daemonheim.
Acording to the Fremennik Saga Nadir, in year 168, Bilrach was on floor 60 and was digging toward floor 61.
Now Bilrach has either found the Rift and/or died. A theory is that he found the Rift but was sacrificed by whoever was down there.
A Q&A at Runefest stated that floor 61 would be released soon and that on the bottom floor with the Rift somebody with a name starting with Z is there. This is presumably Zamorak, although it could also refer to Zaros.