Observing a set of features while training is same as seeing it one time. How? If we use the same training example to train multiple times, it won't bring any change to desired theta values. Can someone provide intuition behind it or some theoretical explanation to back this?

To me, it looks like using the same training example in training could help. Given a training example, weights try to converge but they don't converge to the optimum level because of small learning rate, etc. So, when the model sees the training example again, it may help the weights to converge towards the minima. Thoughts/Intuitions?
This really depends on the type of algorithm you are using. With iterative approaches like stochastic gradient descent this is exactly what does happen. With tree based methods it will not matter except that the interpretation of your hyperparameters surrounding regularization changes by artifically creating a bigger dataset.