Prestige is unlocked when a mission with soul eggs as a reward is completed.
Prestiging grants you Soul Eggs based on your earnings.
After the first 50 Soul Eggs, different strategies exist, but a general rule of thumb is to prestige when the game is slowing down and you have no goals that depend on staying on the current egg.
Prestige Bonus Edit
Prestige Bonus, an Epic Upgrade , gives more Soul Eggs per Prestige. Each level adds 10% more Soul Eggs at restart (e.g. a level 5 would have 50% more Soul Eggs than normal (i.e. 15,000 rather than 10,000)). Prestige Bonus has twenty levels, with a maximum of 200% bonus soul eggs when prestiging.