Paragon is received for resetting with over 70 kittens (you gain 1 point per kitten over 70).
Paragon is also received at a rate of 1 every 1000 ingame years. This has two consequences: Firstly, it allows players to earn paragon during very long runs if they choose not to reset. Secondly, it means that by time traveling into the future, players can farm paragon without resetting.
Every paragon point will give:
The production bonuses are subject to diminishing returns with a cap of 200% (10% for auto production). This cap can be raised with metaphysics upgrades.
The storage bonuses affect every resource except for Temporal Flux and Sorrow. Storage bonuses have no cap.
Paragon can be spent on Metaphysics, one of the game's prestige systems.
188.8.131.52 introduced the idea of burning your paragon, to completely get rid of it. This was done to enable players to get the star version of the Space Oddity Achievements.
As of 184.108.40.206 you can now burn paragon and gain a benefit from it. Burned paragon functions just as regular paragon, but has slightly different limits.
Every point of burned paragon will give: (as of 220.127.116.11)
The bonuses from regular and burned paragon stack additively, so that if you have 150 regular paragon and 75 burned paragon you will have a total paragon production bonus of +225%.
Burned paragon reduces the amount of karma required to build Cryochambers.
Burned paragon also boosts the leader trait bonuses. The formula for the extra bonus is ( square root ( 1 + 8 * burned paragon / 500) - 1 ) / 2 which is then multiplied by the base effect. Philosophers only get 10% of this boost. This boost is subject to limited Diminishing Returns for the Scientist trait (which come into effect beyond 52500 burned paragon) and for the Philosopher trait (which come into effect beyond 1072500 burned paragon).
Burning paragon while in Iron Will mode will immediately end Iron Will. Exception: if you have Space Oddity Insane Version you will stay in Iron Will
Below, the table describes the production bonus percent on Cath, given an amount of paragon, burned paragon, and how many Sephirot upgrades you've purchased. Each improves Paragon and Burned Paragon effects and scaling by 5%.
To get your total effect, add up the effect of regular paragon and burned paragon. The number of sephirots affects the resulting total.