Cosmo is the main source of power in the Saint Seiya universe, but it's more than that. Cosmo is described as a philosophical concept and seems to take inspiration from both western and eastern religious philosophies. Cosmo is the source of life for all living beings and also the reason all matter in the universe exists. It seems that Cosmo may also be related to the movement of atoms, so it's clear that with a sufficiently powerful, Cosmo it's possible to alter the nature of any object, from destroying atoms to stopping them. The origin of Cosmo is the Big Bang that gave birth to the universe, and any time Cosmo is burned inside a body, it's a smaller scale reproduction of the real Big Bang. All human beings have Cosmo deep inside themselves, but only a few are truly aware of it, and even fewer are able to burn it and/or increase it until it explodes.
Being able to burn Cosmo gives a person superhuman abilities like breaking rocks, hitting faster than the speed of sound, firing up to 100 blows per second, etc. But the more the Cosmo is increased, the more extraordinary the power becomes and the harder it is for a human to control. Saints are those who are typically trained with the purpose of awakening their hidden Cosmo and thus becoming able to accomplish extraordinary feats. It doesn't matter how strong a warrior is, without the use of Cosmo they will never be able to stand a chance against even the weakest Saint.
Among Saints, the Bronze Saints have a relatively superficial awareness of their Cosmo and while being far beyond any normal humans, they just scratch the surface of what Cosmo is capable of. Silver Saints are significantly stronger and while they are not yet fully aware of Cosmo, they have skills that greatly outclass a normal Bronze Saint. It's implied that not only Saints awake their Cosmo, but the same is true for warriors of other Gods, although they often don't face the same harsh and deadly training a Saint does to awake his/her Cosmo. At any rate, Cosmo is heavily driven by emotions, so it happens that a sufficiently great willpower or a desperate situation could allow a Saint to greatly surpass his usual limits, although without the proper awareness, this happens to be a brief power increase.
A Saint that is deeply aware of the nature of their Cosmo discovers that Cosmo is actually the seventh of the human senses, after the normal five senses and the sixth that is considered intuition. With this awareness, a Saint is able to draw out the true potential of their Cosmo and achieve exceptionally powerful feats far beyond those of even a normal Saint, like wielding a power destructive enough to pulverize a star, reach the speed of light, or being able to punch billions of times per second. The Saints who are typically aware that Cosmo is actually the Seventh Sense are the Gold Saints and this is the main factor that makes them the strongest among Saints. Although, there are some talented Saints that, even being of lower ranks, are able to awaken to the knowledge of the Seventh Sense. This allows them to fight on the same level as Gold Saints and sometimes they are so skilled as to overcome Gold Saints themselves.
In the crossover series, the effects of the Cosmo Chips on all characters of the Saint Seiya verse has had many effects to this sense, thus preventing it to be used at full power; it can now be awakened as a aura boost that increases one's Cosmo ten times their limited resources, but can only maintain it for at least two hours, possibly more through severe training. Using it depletes one's Cosmo severely, and once run out, it can cause extreme fatigue and exhaustion to the wielder. Utilizing this sense will allow the user to do the following categories: destroy multiple planets or a star with a few punches, moving one's body at the speed of light (or possibly faster), punch a million times per second, or travel across dimensions.
In Saint Seiya Omega, it is discovered that Cosmos can possess an Elemental Attribute (Literary meaning: Attribute) that can strengthen the power of the Cosmos when used. There are seven Elements with their respective Strengths and Weaknesses. The Elements are Water, Fire, Wind, Thunder, Earth, Light and Darkness. Much on a similar sense to the Naruto series, the elemental strength chain is the following:
Water -> Fire -> Wind -> Thunder -> Earth. Light and Darkness are special cases, not affecting (and not being affected by) the other Elements, though they do directly counter each other.
Regardless of the elemental advantage, if one's Cosmos is superior to the opponent then that element will still be superior even if it would be naturally impossible, when Water faces against Earth, the water is easily absorbed by the Earth element, but a strong use of Water can potentially break through Earth.
Element is of great importance in the era of Omega and as noted and evidenced by old veteran Saint Hydra Ichi those who are not aware of their Element or cannot control it, can simply not succeed as Saints or overall users of Cosmos anymore as those who can control their element have noticeable advantage in combat by being capable of using the elements to not only fuel their own sheer power, but also because it can create several new techniques based on the element itself.
For this particular reason, the Palestra a school for Saints puts special attention to Elemental Training, with a strict training regime that not only forces its students to learn Elemental control, but also to strengthen it.
The Element of Cosmos seems to also be related to not only Cosmos but also Physical abilities as well. According to Volans Argo Fire users are terrible swimmers. Moreover as seen in Palestra's training camp known as Cosmo Delta, which is a massive geographical location with several different kinds of nature such as forests, mountains, rivers, etc. The very nature itself can be advantageous or disastrous to Element users. For example Volans Argo could use the water of the river to easily use his attacks, while in the same sense a deep forest with several flowers is detrimental to Water users as the flowers seem to be "draining" the Cosmos of the traveling Saints in the shape of a dark vapor. This same vapor is seen when Aquila Yuna and Dragon Ryuho enter a cave filled with lava, and Yuna eventually falls while walking.
The Gold Saints seem to contain all the Cloth elements.
In Saint Seiya Omega, instead of the Eighth Sense, what comes beyond the Seventh Sense is something which apparently no Gold Saint has ever achieved - Omega. Virgo Fudo spectulates unless the current generation of Saints, regardless of rank, are able to reach Omega, then they would stand incapable of defeating Pallas' primary Pallasites. Due to comments dropped by Genbu and Ikki, Omega is the ultimate Cosmo. Aegaeon notes that it can match a god. In Episode 83 of Saint Seiya Omega, Omega is first seen when Ryuho pushes his Cosmo beyond the maximum which allowed infinite power to well up in Ryuho's body. Even though it could defeat Rhea's army, the power was too sudden for the Saint and he collapsed soon after. Omega is also the power of friendship, meaning that if people work together, they will be able to reach it. In Episode 86 of Saint Seiya Omega, Kouga and his friends awaken part of Omega since they combined their Cosmo as one just to reach infinite power. They were able to transform their cloths and achieve miracles like Ryuho, Souma, Haruto, and Yuna breaking parts of the Phonotector, Eden destroying the war god manifestation blade, and Kouga killing Galia. Kouga states this the power of humanity. Virgo Fudo says that was a gateway of greater power.