The biorhythm is a new feature added in Path or Radiance. Unfortunatly it doesn't affect the game too much and you can go through the game without using it at all.
What does it do?
Neither the game or the manual explains what the Biorythm actually does, however it only affects a units hit %.
Depending on were the icon is on the graph you can gain +/- 5% in hit.
If the icon is on the top line you gain +5%, if it's on the very bottom you get -5% anywhere inbetween gets you 0%.
How do i change it?
You can influence the biorythm by winning battles and taking as little damage as possible. Likewise the biorythm will drop if you perform badly during battles; losing and taking alot of damage.
Do skills affect biorythm?
Yes. The Serenity skill halves the effect therefore giving you a +/-2.5% instead of +/-5%. not very useful then. Tempest however doubles the effect giving you +/-10% hit.