The largest float in the output layer (while the graph is yellow) is the activation. The largest activation in the final layer is the network's "guess". The guess is the index of the last layer, which corresponds to a particular digit.
So I guess during training you're telling it that correct answers should be 1 and the incorrect answers should be 0.
Do the encoding choices that you make regarding the input / output of a neural network influence its performance at all? Maybe for MNIST the way you have it is the most common approach?