Arabic numerals are the number system most commonly used in the world: 0, 1, 2, 3, 4, 5, 6, etc.
The term "Arabic numeral" is a misnomer that originated in 1847. The more accurate term is "Hindu-Arabic numeral", as the origin of the numerals is Hinduism in India between 400 B.C. and A.D. 400. The only connection with Arabs is that they communicated this system to Europe in the A.D. 900s, through Arabian mathematicians. Most Arabs did not use these Indian numerals.
Note that Hindu-Arabic numerals include zero (0): Asian Indians were the first to discover and use this concept.
Westerners such as King John of England learned about Hindu-Arabic numerals as early as A.D. 1200, but there was resistance to converting from the Roman numeral system. It was not until the early 1500s, around the same time as the Reformation, that Hindu-Arabic numerals became widely used in Western Europe.
Numerals in the Arab World
Despite the name as "Arabic numerals", the numerals used in the Arabic writing system are notably different, except for the "1" and "9". In fact, an Arab 5 is designated by "o" which looks like zero, while zero is designated by a heavy dot "•". The basic ten digit symbols are as follows: 
||0||1||2||3||4||5||6||7||8||9||(the Arabic numerals)|
||•||I||Γ||Ґ||ε||o||7||V||^||9||(numerals in the Arab World)|
Note how the Arab 6 looks like a seven ("7"). In typical usage, the Arab numeric symbols are more curved (than shown above), similar to the curvature of letters in the Arabic alphabet. Some examples: 6004 = 7 • • ε or year 2010 = Γ • I • . Those numerals are believed to be derived from hand-signing of numbers, such as 5 (symbol "o") being the circle of touching the thumb to the fingertips.
It is also worth noting that in Arabic writing, numbers are written left-to-right (as they are in the west), whilst words are written right to left.