In making analysis of different networks, one often comes up with interesting intermediate results. These results are mostly in terms of plots and graphs of some complicated phenomenon transformed to some visible representation.
These plots can be saved as images for future reference. However, there are two major drawbacks to this method. First is the inconvenience of keeping and manipulating large files (i.e. taking up space, causing long delays in transfers and problems in distribution), and the second is the difficulty in replicating these results (re-training the network to an exact copy of the time when the results were recorded is almost impossible, whereas similar solutions will be reached every so often).
Saving an exact copy of the network state after training neither takes up much space, or impedes the availability of desired plots.