Patches are game modifications to Phantasy Star Online that change how something behaves in game. This includes graphical fixes or gameplay modifications.
Before applying patches, please make backups of the files you are patching!
Patches are applied by (in the case of PSO for PC), modifying the game's pso.exe executable, manually or through a patcher program. As there are multiple revisions of the pso.exe executable floating around that are largely undocumented, the patches here will need to be manually applied.
Patching for the Dreamcast versions of the game is more complicated and the patches are easily available through connecting to a private server, so they are not documented here yet.
If there isn't a patcher available, you will need to use a hex editor to apply these patches.