To unlock an extra option on the Secrets Menu, collect the required number of Precursor Orbs. Here is a list of the extra options, along with the number of Orbs required to unlock each one:

5 - Toggle Jak's Goatee
15 - Mirror World
30 - Big Head Mode
45 - Small Head Mode
55 - Scrap Book 1
65 - Scene Player Act 1
75 - Vulcan Fury Course
85 - Scrap Book 2
95 - Scene Player Act 2
105 - Peace Maker Gun Course
115 - Scrap Book 3
125 - Scene Player Act 3
135 - Reverse Races
145 - Level Select
155 - Unlimited Ammo
165 - Unlimited Dark Jak
175 - Invulnerability
200 - Hero Mode