Roman numerals are graphic symbols, ie letters, that were used in the ancient civilization of Rome and then in Europe untill the Arabic numbers were introduced, around 1300 AD. For almost 2000 years, this was how the numbers were written in the Roman Empire and Europe.
Numbers that we use today are the so-called Arabic numbers. Example of Arabic numbers: 1, 2, 3, 30, 2013, 5047, etc. They are called so because they entered Europe through the Arab civilization, advanced at that time. Arabs took the numbers from the Indians (Hindu). Indian mathematicians invented (or copied from other unknown sources) the concept of zero, non-existent in other known civilizations. Their system, very simple, yet very powerful, based on only 10 symbols (0 through 9), was on a fast track to be adopted worldwide. The Romans had no representation for zero, they used a word to replace it: "nulla".
It is believed that the Arabic numbers entered Europe through Spain, that was at that time a conquered territory under Arab rule, included into the Great Caliphate. These numbers traveled up here brought by the mathematicians and Arab traders coming into contact with Europeans. Also, it's very possible that Arabic numbers entered Europe through Italian merchants that were travelling frequently into the North Africa, which was also part of the Great Caliphate at that time. Arabic numbers proved to be much easier to work with than the Roman numerals, both in writing and especially when performing calculations.
Roman numerals were taken by the Roman civilization from the Etruscan one, preexisted the Romans in the Italic peninsula. The Romans adapted the alphabet's numerals according to their needs. In fact, the Etruscans themselves copied the numeration system from the Greek (who also copied it from other sources). This system was an acrofonic one - ie a system where the emphasis is on the first letter of a word. The system of representing numbers under an acrofonic numeration system takes only the first letter of the word that designate that number. For example, under the Roman system, C means 100, which is the first letter of the word that designates 100 in Latin, "Centum".
Besides the established forms, some other were still being used, named additives; ie for IV (four) was also used IIII (for XL, which means forty, Romans also used the additive XXXX), and for IX (nine) was also used VIIII (as for ninety, XC, they also used LXXXX). These additive forms have ceased to be used until later in Europe, especially after the advent of printed books and later on after writing standardization efforts with the Roman numerals.
Around 1300, after some 2,000 years of history, Roman numerals were abandoned in favor of the more efficient Arabic numbers. But they continued to be used, in various forms, until today, to represent watch hours, dates, centuries, for numbering chapters in books, write names of leaders and monarchs, or even to make reading numbers impossible for the laymen, and so on...