Training by one batch of examples, what does it mean Say I have a batch of examples, each examples represent a state:

[0.1, 0.2, 0.5] #1st example
[0.4, 0.0, 0.3] #2nd example 
..........
[0.1, 0.1, 0.1] #16th example


I feed through the NN, and then the NN predict the following class:

[move up]   #1st example
[move down] #2nd example
........
[move left] #16th example


And then I take the square loss (which calculated to be 0.1 after taking average over 16 examples), and do backward propagation. 

So, can I assume that each of these examples will assign (or contribute) to a 0.1 loss?
This would mean that there is only one gradient update on your dataset of 16 samples. If you are taking the mean of all the squared errors ( mse ), then the loss of each sample is contributing to the 0.1 loss.