How do PSN levels work?

Earning trophies levels up your account, with each tier of trophy being worth much more than the last. All trophies of the same tier are equal in value.

• Bronze = 15 pts
• Silver = 30 pts
• Gold = 90 pts
• Platinum = 300 pts

The total amount of experience for each trophy level is laid out in this thread. The numbers start low, with level 1 requiring 0, level 2 requiring 200, etc. Level 10 requires 12000, then starting at level 13, the amount of experience required for each subsequent level increases by 8000 until level 26, at which point it increases by 10000 each level indefinitely.

It's also worth noting that after a certain point, there is little to no difference between a person who has a lot of games they barely played and a person with a handful of games they 100%ed. It's just a way for people to complete their games in a competitive fashion.

There are no advantages to having a higher trophy level aside from bragging rights.