Phosphorylation of S6 induces protein synthesis at the ribosome.
P70S6 kinase is in a signaling pathway that includes mTOR (the mammalian target of rapamycin). mTOR can be activated in distinct ways, thereby activating p70S6K. For example, branched chain amino acids such as leucine are sufficient to activate mTOR, resulting in an increase in p70S6K phosphorylation (and thereby activating it). mTOR is also in a pathway downstream of the kinase Akt. Akt is typically activated upon stimulation of a cell with a growth factor (such as IGF-1). Akt then activates mTOR (by inhibiting the Tsc complex), leading to p70S6K activation.
We also found a paper showing that downregulation of S6 kinase also results in a decrease in protein translation in yeast (but I'm waiting for Matt Kaeberlein to email me the slides from yesterday).