The train is a mechanic in the series.
The train system allows the protagonist to travel around numerous locations in Tokyo. He will have to pay a small fee each time he switches between a different area outside of Yongen-Jaya, Shibuya and Aoyama-Itchome due to the limitations of his transit pass.
If protagonist is unable to pay the train fee to return back home at Yongen-Jaya, Morgana will use his secret savings to help him pay the needed amount to travel.
On certain days, the protagonist will be able to take a free seat on his commute to school. On these occasions, he'll be able to read a book. These events serve as an additional time slot, separate from the usual Daytime or Evening periods. The dates the protagonist takes a seat differ between Persona 5 and Persona 5 Royal.
The ability to find free seats is first demonstrated on April 16th, but the protagonist cannot read at that time.