TSMC is the biggest semiconductor foundry in the world, and the trials will test whether it will be able to meet the huge demand for Apple chips. The particular chip in question, the Apple A6X is what Cupertino introduced in the fourth-generation iPad.
Interestingly, TSMC is also rumored to be contracted to make 20nm quad-core chips for future Apple devices. Devices like the iPad are expected to use such silicon, while the iPhone is more likely to remain on a dual-core architecture.
source: Commercial Times via 9to5Mac