Delta Rune

The Delta Rune is an emblem that represents the Dreemurr royal family. It shows an orb between two wings and three triangles beneath it; the bottom middle triangle being inverted.

It is first seen on Toriel's dress, foreshadowing her role in the story, as the familiar symbol appears in other places.

Symbolism
The Delta Rune is said to symbolize a prophecy that predates written history, although the original meaning has been lost in time. The only thing that can be said with certainty is that the triangles below symbolize the monsters of the Underground; although many believe the winged circle to symbolize an "Angel." The prophecy narrates of an "Angel" who has seen the surface, who will descend into the Underground and make it empty of monsters. This prophecy has two interpretations: one where the "Angel" destroys the barrier and brings freedom to the monsters; and one where it's an "Angel of Death", who massacres everyone in the Underground.

Trivia

 * "Delta Rune" is an anagram of "Undertale."
 * The Delta Rune actually makes an earlier appearance than on Toriel's dress. It appears during the introduction sequence, on a monster's shirt, and it is shown over the doorway that is entered in the first room.
 * The Delta Rune bears a resemblance to the royal crest of the Zelda series, both with three triangles and a winged figure.