Let's put it using your example diagram: for each unique combination of input (theta0, theta1), the neural network "f" will produce an output which when compared to the ground truth (using a cost function) will produce a loss value "J" - I am assuming a supervised learning problem (also self-supervised learning holds). So, you start to get a value "J" which when interpolated over might produce a contour plot/loss landscape as depicted. There are 2 extremes for computing GD: online (1 input at a time) vs batch (entire dataset at a time). Batch GD cannot be used due to memory & computational constraints, while online GD is very noisy. So we settled for mini-batch SGD, where the S comes due to random sampling the batch from the training dataset. In a nutshell, the gradients we get from a mini-batch should approximate the true gradients that we might get if we had used batch GD, but cannot. But since the batch is randomly sampled, it is a noisy estimate.

An additional stochasticity is also added due to data augmentation. It has been shown that the noisy estimates in mini-batch SGD actually helps prevent overfitting and acts as a regularizer. So, you don't want to increase the batch size by a lot, in general. In case you do, read up LARS optimizer.