On one hand, there is a PC needed to flash JetPack from (not necessarily doing deep learning training). The specs for that machine should be Ubuntu 16.04 x86_64 with at least 10GB of free disk space, and ideally any CUDA-capable discrete GPU for installing the host-side CUDA toolkit for compiling the CUDA samples. See here for the JetPack install docs with the system specs.
The machine that you use for deep learning training can be the same as you use for flashing JetPack to your Jetson, but it doesn’t have to be (for example, many folks train in the cloud via AWS or Azure). Typically the specs of an effective deep learning training system will include a fairly recent GPU (like from Kepler/Maxwell/Pascal/Volta family), ideally with 8GB GPU memory or more and depending on the size of your datasets, a decent-sized SSD (typically 512GB-1TB or more) along with 32/64GB system RAM. Ubuntu 16.04 or 14.04 is also common on the training machine. You can certainly use a lower-end training machine too, the training just will take longer (as long as there is some NV GPU in there - otherwise it will likely take unbearably long for training networks for tasks like image recognition, object detection, segmentation, ect.).