The Entity is some mysterious being that may have created the Gates in Chrono Trigger and wanted Crono, Marle, Lucca, Robo, Frog, Ayla, and Magus (if the party decides not to fight him) to witness the events they saw.
As Crono's party progresses through the game, they believe that Lavos is the one leaving the Gates behind. However, after the party reunites with Robo in the Present after growing the forest for Fiona, Robo explains that over the past 400 years he spent growing the forest, he believes now that it was not Lavos that created the Gates, but that some entity wished for them to witness the events they have seen. Alternatively, he says, the entity may have wished to see them for itself or it was reflecting on the days of its past. However, even if Lavos did not open the Gates, his fate is bound to that of the one who did as Lavos played a role in every age they visited. Robo goes on to say that it is unknown to him whose memories these are, though it is likely an entity greater than any of them.
After defeating Lavos, during an ending Lucca says that she feel the entity is finally at rest, which Marle says she feels as well.
It has been argued on "who" or "what" this entity is. The Earth itself is a very viable candidate for being the entity as it would feel at rest once Lavos is destroyed, as it would no longer be in danger. The Earth would also be able to create the gates on itself, and Robo was reflecting on this while he was re-growing the forest. This is supported by the original Japanese version of the dialogue for the final battle, which mentions how Lavos is a parasite that feeds off the living Earth.
The entity could also just be that, an entity similar to that of a God.
Some believe the Entity could also be Schala connected to the Dream Devourer. Aside from the name linking it to dreams, Schala and by extension the Dream Devourer is outside of time. Since Schala has incredible power it could be supposed that she wanted to save the world and set things right, destroying Lavos once and for all.
It is also possible that the entity is actually the player of the game. After completing the game one would be at rest.