common terms

Karate : Empty Hand
Dojo : Training hall 
Shihan : Senior instructor
Sensei : Teacher
Sempai : Senior student 
Gi : Karate Suit
Kyu : Levels below Black belt, counting down to 1st kyu, usually from 10th kyu 
Dan : Steps showing mastery of the art, starting from 1st dan 
Rei : Bow 
Yoi : Ready
Hajime : Begin 
Yame : Stop
Mawatte : Turn 
Narande : Line up
Kihon : Basic
Kata : Form 
Kumite : Sparring

Rank System

Around the 1920's, Funakoshi adopted the Kyu/Dan system, along with the Judoka's uniform, the gi that had been developed by Kano Jigoro. This system used colored belts as an indication of rank. Originally, Karate had only 3 obi (belt) colours. White, Brown and Black, with several ranks of each. Here is the original belt system.

DOJO KUN: Seek perfection of character, be faithful, endeavour, respect others, refrain from violent behaviour!

Kata

(literally: "form") is a Japanese word describing detailed patterns of movements practiced either solo or in pairs. Kata are used in many traditional Japanese arts such as theater forms like kabuki and schools of tea ceremony (chado ), but are most commonly known for the presence in the martial arts. Kata are used by most traditional Japanese and Okinawan martial arts , such as aikido , iaido , jodo , judo , jujitsu , kendo and karate . Other arts such as T'ai Chi Ch'uan Taekwondo feature the same kind of training, but use the respective Chinese and Korean words instead. 

Shotokan Kata

Taikyoku Shodan : Great Ultimate beginning step (basic) 
Heian Shodan : Peaceful Mind beginning step 
Heian Nidan : Peaceful Mind 2nd step
Heian Sandan : Peaceful Mind 3rd step 
Heian yondan : Peaceful Mind 4th step
Heian Godan : Peaceful Mind 5th step
Tekki Shodan : Horse riding beginning step 
Bassai Dai : To Penetrate a Fortress (Major) 
Jion : Kind and Graciousness 
Enpi/Empi : Flight of the swallow
Kanku Dai : To Look At the Sky (Major) 
Hangetsu : Half-moon

See Kata Library for videos