The skill descriptions have been updated since this question was asked to be more informative (and in particular you can now see your solipsism threshold just by mousing over one of these skills), but for the sake of completeness...
The overall benefit of the Solipsism skills is that they let you use your best stats to boost or replace the rest. Psi instead of health, willpower instead of consistution, mental save instead of magical or physical saves or armour. The drawback of this is that if your psi drops below the solipsism threshold, you lose 1% of your speed for each percentage point below the threshold - and the more solipsism skills you learn, the higher the threshold gets (and thus the sooner the penalties will kick in, and the more severe they are at 0 psi). Additionally, all of the skills increase how much psi you get per point of willpower, and decrease how much HP you get per point of constitution.
For the specifics of the skills:
- Solipsism: Increases Psi, reduces HP. A percentage of all damage and healing affects Psi instead of HP.
- Balance: Lets you use your Mental save to boost your Physical and Magical saves. At level 5, completely replaces them.
- Dismissal: Reduces incoming damage by 50% on a successful mental save.
- Clarity: Boosts your global speed based on how full your psi bar is.
The overall theme of the skill tree is that the more heavily you invest in it, the more benefits you get for high willpower, mental save, and psi - but the more harshly you are penalized if you let your psi run low.