The first and foremost advantage that TPUs offer over GPUs and CPUs is performance. Google compared the TPU performance to a server-class Intel Haswell CPU and a NVIDIA K80 GPU running the benchmark code representative of 95% of the inference workload; it found that the TPU is 15-30 times faster than both NVIDIA's GPU and Intel's CPU.
The second important parameter is the power consumption. It is important to reduce power consumption since it has a twofold energy benefit: not only does it reduce the amount of power consumed, it also saves power by reducing the cooling cost to dissipate the heat generated while processing. The TPU/CPU per watt performance shows a 30-80 times improvement over other CPU and GPU configurations.
Another advantage of TPUs is their minimal and deterministic design since they have to execute only one task at a time.