Bins are the number of vertical bars you are observing on the graph. The total error from neural network ranges from -0.2222 (leftmost bin) to 0.1968 (rightmost bin). This error range is divided into 20 smaller bins, so each bin has a width of
(0.1968-(-0.2222))/20 = 0.02095.
Each vertical bar represents the number of samples from your dataset, which lies in a particular bin. For example, at the mid of your graph, you have a bin corresponding to the error of -0.00166 and the height of that bin for validation dataset is 10. It means that 10 samples from you validation dataset have an error lies in the following range.
(-0.00166 - 0.02095/2 , -0.00166 + 0.02095/2)
(-0.012135, 0.008815) < the range of the bin corrosponding to -0.00166
Similarly, for other bins, you can interpret the result.
