Playstation Network, or PSN, is the online video game network from Sony that operates on the Playstation 4, Playstation 3 and Playstation Vita video game systems. Occasionally, PSN is down for maintenance or because of server load issues. If you are having trouble accessing the Playstation Network, check the status of PSN on Sony's official support page.
The official Playstation knowledge center, which displays the current status of PSN, offers several other options for checking the current state of PSN. The official Playstation support twitter account, @AskPlaystation, regularly posts updates on the operating status of PSN. If Playstation Network is indeed down or undergoing maintenance, this twitter account posts a status update. Finally, if neither of these official sources provide the desired information, there are unofficial sources that may be of help. Downdetector is a website that compiles user feedback on a variety of services, PSN included. If you are having issues logging into PSN, it is likely that others have as well and have shared their experiences on this website. From this source you can't get information on why these issues exist, but you get a sense of whether the problem lies on your end or if it is a widespread issue.