"Passenger Information System" is the experts' name for all kinds of devices onboard public transportation vehicles providing more or less important information to the travellers. For historical reasons, the expression notably excludes the Public Announcement System, so, usually, PIS means visual displays only. If you want to, the platformside displays at bus or railway stations count as parts of the PIS, too.
The most important information that is to be transmitted by a PIS is where the vehicle is going, where it will stop and what the next stop is. On buses, this is usually all; on trains, where the vehicle and the distances between stops are much larger, PIS becomes more important, especially if the train consists of parts that separate at a station to go in different directions.
Cardboard
The first PIS-like system on trains were simple cardboard panels with destination and stops printed on them in large print. They were (and are, where they are still in use) put into frames behind the train's windows by the personnel. Space on them is, of course, limited, and the system is somewhat clumsy and error-prone, especially, if the right panel is not at hand when it's needed.
Dot-matrix displays
As a solution to these problems, computer-controlled dot-matrix displays were developed. While electro-mechanical flip-chip dot matrices and other flip-board displays knew some use, today LED matrices are used almost exclusively.
A modern commuter train may have dozens of PIS displays. On the outside, the destination is usually displayed on both sides of each car, and in or above the front windows of the end cars (resp. loco and cab car). Inside, there is a PIS above the connection doors, i.e. two per car, so passengers facing either direction will see a destination display.
Long-distance trains feature PIS, too, nowadays. As a case in point, Deutsche Bahn's ICE 3 high speed train has red-on-black LED matrix displays displaying the destination, train number, car number and a marquee of all the train's stops next to each door. Similar multifunctional displays can be found inside, near the entrance doors. At each end of each car, large LED matrix displays overhead can display the same information in a different layout or various other information; when switched off, these displays disappear, as they are mounted behind semitransparent mirror glass.
Additional information
Of course, the PIS can display more than just fixed destination names. State-of-the-art systems change between displaying the current time and date, the car's destination (not necessarily the same for all cars in the train, see above), the next stop and all kinds of announcements deemed not important enough to justify annoying the passengers via the P.A.; on the ICE 3, this can be the current speed, reminders not to forget any briefcases or umbrellas, advertisement for the onboard snack bar or the audio programme etc. etc.
Video
The most advanced kind of PIS know to mankind is installed on, for example, Hannover's trams (operated by üstra). Eight full-colour video screens are installed under each car's ceiling; they display all kinds of passenger information, entertainment programmes, weather reports, commercial spots etc. For my taste, it's a little too intrusive; it's much harder to ignore a repetitive full-screen video loop than a repetitive LED-matrix display.