Paragon is received for resetting with over 70 kittens (you gain 1 point per kitten over 70), or for every 1000 in-game years.
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.
Paragon can be spent on Metaphysics, one of the game's prestige systems.
184.108.40.206 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 220.127.116.11 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 18.104.22.168)
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 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.
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.