TensorFlow is an open-source machine learning framework. But TensorFlow can be used for more than simply running models on mobile devices—it can also be used for training models. For running it on mobile devices, we have TensorFlow Lite. The models that are exported from Azure Cognitive Services are for TensorFlow Lite. There are also Xamarin bindings for TensorFlow Lite that are available as a NuGet package.
More information about TensorFlow can be found in the official documentation at https://www.tensorflow.org/.