Infinity is one of the five essential entities within the Marvel Universe alongside Eternity, Death, Oblivion,Master Order, Lord Chaos, and Galactus. These beings called each other brothers and sisters, though due to their nature as personifications of abstract concepts, they were not family in any conventional human sense.
Infinity was the personification of space and its expansion. She was the sister/other half of Eternity, who was a personification of time (also presented as the personification of reality in the universe). Together they represented all time and space in the Marvel Universe, while their siblings Death and Oblivion represented death and non-existence. It was revealed that Eternity and Infinity were in fact two different aspects of the same being, when they appeared as a single entity during the Infinity War.
Eternity and Infinity were in constant competition with Death and Oblivion, with Galactus providing a balance between the two sides of the struggle. This competition was not hostile, but an inevitable result of their natural purposes. Where Eternity and Infinity tried to expand life and the universe, Death and Oblivion desired to reduce it, usually to a point where there was an exact balance between life and death, but sometimes they seemed to want the complete end of existence.
In this conflict, Oblivion endowed his champion, Maelstrom with some of his power, making him his avatar. Maelstrom tried to end Infinity. To stop him, Infinity made Quasar her own avatar. Quasar won and Oblivion and Infinity came to a new agreement.  The role of Infinity was thought to be one of great importance to the workings of the Marvel Universe, but exactly what her role is has yet to be defined.
Known Functions Of Infinity
As Eternity represented time, Infinity represented space. Like most abstracts, Infinity's purpose was kept extremely vague and her lack of appearances gave her little development. However, certain appearances have implied that Infinity is connected with the expansion of life much like Eternity is connected with the progression of evolution, concepts that are often at odds.
Infinity's and Eternity's "offspring", Eon, was charged with protecting the Celestial Axis (the pattern of life energy threading through the universe, known to the Asgardians as the World Tree, Yggdrasil) and nurturing the evolution of sentient life of the universe. This led to Eon searching out and appointing various beings to be his champion, known as the Protectors of the Universe, anticipating and conquering major threats to life. Past champions included Captain Marvel, Quasar and most recently Gravity.
Infinity also had a relationship with the "gods", races of mystical beings throughout the universe. On Earth, the gods were born of Demiurge, the sentient life force of Earth's biosphere that emerged when the Earth was formed. In the Quasar series it is revealed that the Asgardian Allfather Odin had tapped into a fraction of Infinity's power creating the "Infinity" that appeared in the Thor series. This being, while wielding a fraction of Infinity's power, did not represent the actual entity Infinity.
The Eternity of Earth-616, as well as its alternate reality counterparts, was annihilated by the Beyonders.