Deep Neural Networks (DNNs) have had a significant impact on domains like autonomous vehicles and smart cities through low-latency inferencing on edge computing devices close to the data source. However, DNN training on the edge is poorly explored. Techniques like federated learning and the growing capacity of GPU-accelerated edge devices like NVIDIA Jetson motivate the need for a holistic characterization of DNN training on the edge. Training DNNs is resource-intensive and can stress an edge's GPU, CPU, memory and storage capacities. Edge devices also have different resources compared to workstations and servers, such as slower shared memory and diverse storage media. Here, we perform a principled study of DNN training on individual devices of three contemporary Jetson device types: AGX Xavier, Xavier NX and Nano for three diverse DNN model--dataset combinations. We vary device and training parameters such as I/O pipelining and parallelism, storage media, mini-batch sizes and power modes, and examine their effect on CPU and GPU utilization, fetch stalls, training time, energy usage, and variability. Our analysis exposes several resource inter-dependencies and counter-intuitive insights, while also helping quantify known wisdom. Our rigorous study can help tune the training performance on the edge, trade-off time and energy usage on constrained devices, and even select an ideal edge hardware for a DNN workload, and, in future, extend to federated learning too. As an illustration, we use these results to build a simple model to predict the training time and energy per epoch for any given DNN across different power modes, with minimal additional profiling.