The origin of the stupa (tib. Chörten mChod rten) can be traced to ancient Vedic India. It was customary to put the ashes of cremated bodies into tumuli.
The Buddhist stupas, however, are not mere elaborations of the burial mounds. They function as a symbolic representation containing relics, not as a container of relics that has symbolism. The relics sanctify the structure endowing it with the consecrated quality that the living being (of whose these are the relics) possessed. Some Buddhist texts refer to stupas built containing the relics of past Buddhas. So one can assume that stupas existed already during Shakyamuni Buddha's life, although in much more simple forms than we know today.

According to the Mahaparanirvana Sutra it was the historical Buddha himself who determined that his physical remains should be put into a stupa at the crossing of four main roads.
After Buddha's passing away at Kushinagara, in order to prevent quarrels over his relics they were equally divided among the eight kingdoms of Madhadesha where the Buddha mainly had taught and travelled. From these eight portions of the cremated remains of the Buddha, originally eight stupas were built. Some 20 years later, concerned about the safety of the relics, the relics of seven stupas were collected and deposited in one stupa built in Rajagriha. (The eighth stupa was left untouched because it was protected by a naga.)
King Ashoka, after his conversion to Buddhism, decided to built 84.000 stupas containing relics of the Buddha. Therefore the king had the stupa opened which contained the relics of seven of the eight original stupas. Using these relics, 84.000 stupas were constructed in all places special to the Buddha and Buddhism.

The general structure of the stupa was laid out by the Buddha himself: First he made four folds in his robe and laid the resulting four layered square on the ground to mark the base of the stupa. On top of that he placed his inverted alms bowl representing the dome or flask section; on top of that the Buddha placed his mendicant's staff to illustrate the wheels and umbrella sections. Later stupas, although considerably more elaborate, did not change these basic components.

Since reliquary stupas contain remains of a holy person, they proclaim the presence of the Buddha in order to help generate confidence and compassion.
The stupa is the representation of the enlightened mind of the Buddha, the Dharmakaya. In this way the Buddha's enlightened mind is said to manifest in the form of stupas. Tibetan sources enumerate five different types of stupas:
1. The Spontaneous Naturally Arisen Stupa
2. The Incomparable Stupa
3. The Blessed Stupa
4. The Stupa Generating Attainments
5. The Stupa of the Vehicles

Concerning the latter there are three Stupas of the Vehicles which are the manifestations of the Buddha's path systems. The third of these stupas is the so called Mahayana Stupa. As the manifestation of the complete path of the Tathagatas it is also known as the 'gone to bliss stupa'. In order to exemplify all the qualities of those gone to bliss, there are eight types of the Mahayana Stupa. These eight types are commonly known as "the Eight Stupas" which are found throughout regions of Tibetan culture. They have become the popular stupas of the present day.

These eight are:
1. The Piled-up Lotus Stupa
2. The Enlightenment Stupa
3. The Auspicious Many Doored Stupa
4. The Miraculous Subjugation of Heretics Stupa
5. The Descent from Heaven Stupa
6. The Reconciled Schism Stupa
7. The Bestowal of Blessings (or Victorious) Stupa
8. The Beyond Sorrow Stupa

The eight stupas represent different aspects of the Buddha's Mahayana teachings and the eight extraordinary deeds of the Buddha (these are: birth, enlightenment, first discourse, display of miracles, descent from heaven, reconciliation of the sangha, bestowment of blessings and parinirvana; all together they are physical manifestations of Buddha's enlightened mind). Each of them has its own shape which corresponds to a particular deed by the Buddha. They may be found all together in one place or just built singular in one particular location.

The Enlightenment Stupa is the most basic of all the Mahayana Stupas and serves as the standard for the other seven. When a great teacher has passed away his relics are most often enshrined in this type of stupa. By enshrining the relics of a great teacher inside the stupa, it becomes empowered by the Buddha himself. So the Buddha's eternal presence is contained in the stupa. Building a stupa is considered as one of the greatest work of merit.
The stupa is depicted as the embodiment of the Buddha and it also evokes the memory of the Buddha and his teachings, but above all the stupa represents the complete path to enlightenment which results in the enlightened mind of the Buddha, the Dharmakaya. Every part of the stupa represents a distinctive aspect, such as the 'four immeasurables' and the '37 aspects of the path to enlightenment', 'the ten knowledges', 'the ten powers' and so on. According to a comment in the Kangyur: "The nature of the stupa is that which thoroughly holds all the Dharmakayas of the Tathagatas throughout the different time periods, for the sake of the universe".

The act of paying respect and homage to the stupa is no different than honouring and worshipping the Dharmakaya of all enlightened beings. For the practitioner the stupa is important as an object to be worshipped and respected in the same way as worshipping the Buddha himself. By viewing the stupa in this way one is able to generate merit which assists the practitioner to the highest goal of enlightenment.

(Most information of this piece of writing has been drawn from "The Buddhist Stupa: It's History, Dimensions and Symbolism According to Tibetan Sources" by Lori J. Cayton)