This will increase most of the stats for each Ability casting you do. The effect is cumulative -- your second cast gets +x% boost, your third cast gets +x*x% boost, etc. Up to 75%.
This doesn't need to be the same ability -- any of your 4-5 cards (including the rented one) will work, as long as they're consecutive. (does this include multi-strike abilities?) Normal attacks, Job Change Recast, Elemental Drive, or the end of your turn will drop this back to 0%.