Overview:

What we know as Arabic numerals were neither invented nor widely used by the Arabs.  Instead, they were developed in India by the Hindus around 600 AD.  However, because it was the Arabs who transmitted this system to the West, the numerals became known as "Arabic".
 
 

From top -  Modern Arabic (western) Early Arabic (western) Arabic Letters (used as numerals) Modern Arabic (eastern) Early Arabic (eastern) Early Devanagari (Indian) Later Devanagari

Significant Traits:

Arabic numerals greatly eased arithmetic computations because of the following significant traits:

Positional:

The Arabic numeral system is positional in that the actual value of a numeral is determined by its placement within the written number. Thus, 2 in 323 stands for twenty, while 2 in 233 stands for two hundred. 
 

Single Symbol System:

In the Roman, Egyptian, and Greek numeral systems the number 323 was expressed like this: 

Egyptian:  999 nn III 

Greek: HHH ÆÆ III 

Roman: CCC XX III 

The Indian contribution was to substitute a single symbol (in this case meaning "3" and meaning "2") indicating the number of signs in each cluster of similar signs. Using this system the Indians would express Roman CCC XX 111 as: 3 2 3. 

Zero: 

This new way of writing numbers was efficient and space saving, but not without flaws. The Roman numeral CCC II, for instance, presented a dilemma. If a 3 and a 2 are substituted for the Roman clusters CCC and II, the written result was 32. Although one can see that the number intended was not thirty-two but three hundred and two. The Arab scholars perceived that a sign representing "nothing" was required, because the place of a sign gave as much information as its unitary value did. The place had to be shown even if the sign which showed it indicated a unitary value of "nothing." It is uncertain whether the Arabs or the Indians filled this need by inventing the zero, but in any case the problem was solved: now the new system could show neatly the difference between XXX II (32) and CCC II (302).
 

Introduction to Europe:

It is not known exactly when the new number system first came to Europe, although there is evidence is that it came many times between 976 and 1275. The oldest dated European manuscript containing Arabic numbers is the Codex Vigilanus written in Spain in 976. And even though the French monk and mathematician Gerbert (940-1003) who became Pope Sylvester II in 999, also used them in several of his writings, they did not yet come into common use. 

In 1202 Leonardo of Pisa (also known as Fibonacci) published his Liber Abaci, a book of arithmetic and algebraic information.  Al-Khwârizmî's book was a major influence on Fibonacci. In spite of the popularity of Fibonacci's book among scholars, the earliest French manuscript to use the new number system was written in 1275.  In western Europe merchants continued to use Roman numerals in keeping their books.  The Greek system of numerals remained popularin regions around the Adriatic for many years more. 

*The Medieval Technology Pages 
Arabic Numerals 
http://scholar.chem.nyu.edu/~tekpages/arabnums.html

*http://islam.org/Mosque/IHAME/Ref6.htm
Arabic Numerals

http://math.truman.edu/~thammond/history/NumberSystems.html
Number Systems - Mathematics and the Liberal Arts

http://www.gosai.com/chaitanya/saranagati/html/vishnu_mjs/math/math_4.html
Evolution of Arabic (Roman) Numerals from India

http://www.islamic-paths.org/Home/English/History/Literature/Arabic_Numerals.htm
Arabic Numerals
An Historical Perspective

Hindu-Arabic Numerals
http://www.scit.wlv.ac.uk/~cm1993/maths/mm2217/han.htm

*http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html
Fibonacci
University of St. Andrews