History:
The three points are represented on inscriptions since times immemorials, throughout the world. Nicholas Roerich added a circle around the dots and presented this symbol to the world as the Red Cross of Culture (Cult of Ur = Light).

Meaning:
One of the first meaning is The three are One.
Any unit or form is crossed by three seeds: Life, Relationship, Activity.
The red color points out life, the first aspect, transcendance, that which goes through and sustains existence.
As wrote Nicholas Roerich, it represents Past, Present and Future in the circle of eternity, or art, science and religion in the circle of Culture. And this symbol will find an echo in every heart.

Significance:
Peace, Strength, Plenitude.
As says the rule 12 in Rays and Initiations, this symbol will replace the Cross. The cross symbolises radiation, yet also a cut in substance, threrefore an arduous detachement. The three dots inside the circle can be perceived in depth as a transversal view. This points out intensity in action, tension-to-be, link of the Self to its expression.

More indications:
“The ruler of Shambhala is the Crest of the Banner and the Summit of Life. Accept the Ruler of Shambhala as the manifestation of life; thrice I say- of life !“
HIERARCHY §5
“Thus, when We introduce into life a new affirmation, one should strive with the entire spirit on the path of fulfilment of the Highest Will. Hence, when We affirm the great significance of the Banner of Peace, it must be adopted in spirit.“
HIERARCHY § 339
“Thus, during the Epoch of Fire, when Light battles with darkness, the manifestation of the Banner of Peace is that fundamental sign which will give a new step to humanity.“
HIERARCHY § 377
“Those who do not comprehend the new ways are greatly in need of understanding the Epoch of Maitreya. The Banner of Peace and of the Lords will open all ways !“
HIERARCHY § 390

RULE 12 for groups:
"Recognition of the successful work of the New Group of the World Servers will be accorded by the Hierarchy, and the testimony of the recognition will be the appearing of a symbol in the aura of the group - of the entire group. This will be a symbol projected by the Hierarchy, specifically by the Christ. What that symbol will be it is not for me to say. ... It is the "mark of the Saviour" and it will embody the mark or indication (the signature as the medieval occultists used to call it) of a new type of salvation or salvage. Up till now the mark of the Saviour has been the Cross, and the quality of the salvation offered has beeen freedom from substance of the lure of matter and from its hold - a freedom achieved only at a great cost. The future holds within its silence other modes of saving humanity. The cup of sorrow and the agony of the Cross are well-nigh finished. Joy and strength will take their place. Instead of sorrow we shall have a joy which will work out in happiness and eventually to bliss. We shall have a strength which know naught but victory ..."
Alice Bailey R5 p 233

The Banner of Peace

"This sign of the triad which is to be found all over the world may have several meanings. Some interpret it as a symbol of past, present and future, enclosed in the ring of Eternity; others consider that it refers to religion, science and art, held together in the circle of Culture. But whatever the interpretation the sign itself is of the most universal character.
The oldest of Indian symbols, Chintamani, the sign of happiness, is composed of this symbol and one can find it in the Temple of Heaven in Peking. It appears in the Three Treasures of Tibet; on the breast of the Christ in Memling's well-known painting; on the Madonna of Strasbourg; on the shields of the Crusaders and coat of arms of the Templars. It can be seen on the blades of the famous Caucasian swords known as "Gurda".
It appears as a symbol in a number of philosophical systems. It can be found on the images of Gessar Khan and Rigden Djapo; on the "Tamga" of Timurlane and on the coat of arms of the Popes. It is to be seen in the works of ancient spanish painters and of Titian, and on the ancient ikon of St Nicholas in Bari and that of St Sergius and the Holy Trinity.
It can be found on the coat of arms of the city of Samarkand, on Ethiopan and Coptic antiquities, on the rocks of Mongolia, on Tibetan rings, on the breast ornaments of Lahul, Ladak and all the Himalayan countries, and on the pottery of the neolithic age.
It is conspicuous on Buddhist banners. The same sign is branded on Mongolian steeds. Nothing, then, could be more appropriate for assembling all races than this symbol, which is no mere ornament but a sign which carries with it a deep meaning.
It has existed for immeasurable periods of time and is to be found throughout the world. No one therefore can pretend that it belongs to any particular sect, confession, or tradition, and it represents the evolution of consciousness in all its varied phases.
When it is question of defending the world's treasures, no better symbol could be selected, for it is universal, of limitless antiquity and carries with it a meaning which should find an echo in every heart."

Nicholas ROERICH