Shotokan is a style of the Japanese martial art of Karate, and is the most widely-practiced style in the world. Shotokan was founded by Gichin Funakoshi, a school teacher originally from Okinawa in the early part of the 20th century, based on influences from his native Okinawa as well as other traditions, including some from China. Funakoshi, of course, didn't call his art "Shotokan", but rather he simply called it "Karate" meaning "Empty Hand". Indeed, most styles of Karate acknowledge Funakoshi as the father of modern Karate. The name Shotokan comes from Funakoshi's pen-name of "Shoto" meaning "pine waves". It is believed that the name was actually applied by one of Funakoshi's pupils to indicate the style taught by Funakoshi himself.
Shotokan is considered to be a more traditional style of Karate, and is characterised by deep stances and quite powerful techniques. There is heavy emphasis on Kata (pre-arranged sequence of movements against imaginary opponents - see the Kata sections in the menu) within most organisations. Kata is an essential part of Karate training, and makes up part of the symbiant circle: Kihon (basics), Kata, and Kumite (sparring).
There have been many changes over the years to what we know today as modern Shotokan. Originally, the style contained numerous throws, locks, and take-down techniques. These are, sadly, left to the history books, but many of these techniques still exist in the Kata, though subtly disguised as fancy jumps and spins.
While there are literally hundreds of Shotokan organisations world-wide, most follow the common practices of two primary "schools" of thought: The Japan Karate Association (JKA) primarily following the principles and techniques taught by the late Sensei Nakayama, and the Shotokan Karate International Federation (SKIF) following the instruction of Sensei Kanazawa. These are the two largest organisations, but both have had several "break-away" organisations formed along similar practices. As a result there are essentially two main methods in Shotokan, referred to as the "JKA Style" and "Kanazawa Style". (Kanazawa is the chief instructor of SKIF). Since there is no such thing as a "right and wrong" way of doing something in martial arts, which version is practiced is purely a matter of personal preference (and in some cases geographic availability).
Logos and emblems are widely used to show some form of identity or association with a group. One can often identify which "school of thought" a particular organisation adheres to by the choice of organisational logo. In most cases (though there are exceptions) organisations aligned with the "JKA" style use the Inyo or symbol of the rising sun. Organisations aligned with the SKIF (Kanazawa) style tend to use the tora no maki or so-called "Shotokan Tiger".
How Much Training?
The practice of Karate is a purely individual thing. People do karate for a number of reasons, mostly personal to themselves. As a result, the amount of training one should do is entirely up to oneself. There is no requirement for a person to grade if they don't want to. There is equally no requirement for a person to attend two-hour training sessions 7 days per week for the rest of their life. Set your own goals. The instructor can help you achieve those goals and will make suggestions on how to attain them, but these are suggestions.
In general, if your ambition is to reach the level of black belt, and you train two or three times per week, you can expect to achieve 1st dan in around four or five years. Some may do it earlier, some may do it later, and others may not make it at all, but this is an average.