May be a lot of foreigners think that there are only Shinkansen bullet trains are running in Japan, connecting the cities. However, there are only 9 Shinkansen lines in Japan and most cities are connected by limited express - Tokkyu in Japanese. If you translate tokkyu(abbreviation of Tokubetsu kyuko) to English, it should be SPECIAL EXPRESS.
Then, JR's fare system is not as same as the European one. You have to pay the fare ticket(joshaken) if you want to take the local trains or rapid trains(or any train type includes rapid). However, if you want to ride Shinkansen, limited express or express, you have to pay also the supplement for Shinkansen or limited express = Tokkyu-ken(Limited express ticket) or kyuko-ken(express ticket) for express trains.
Luckily for all Japan Rail pass holders, you do not need to pay the supplement for any regular service Shinkansen, limited express or express trains. The only concern is that you cannot take the NOZOMI or MIZUHO Shinkansen trains running on Tokaido and Sanyo Shinkansen lines. If you want to take these trains, not only you have to buy the limited express ticket but also have to pay the full fare ticket. If you want to take Nozomi or Mizuho from Hiroshima to Tokyo, you have to pay JPY 18040(non-reserved seat) additionally. JPY 18040 is 62% of the 7 days pass(2nd class) price.
Then, please note that there are limited express trains which have only RESERVED cars, which means seat reservation is compulsory. Anyway, we recommend to make the seat reservation at least one day before your trip for all kinds of limited expresses.