Increasing a character's Bloodweb prestige level has the following effects:
Reset the progress of this character to level 1.
Unlock a prestige reward for that character.
Lose all items, add-ons, Perks & Offerings for this character.
Slightly increases the odds of getting better items on the Bloodweb.
Teachable Perks will stay available to all other characters.
Once you prestige, you will keep all four of your perk slots. You can prestige up to three times.