Roman numerals are a method of writing numbers that date back as far as 800 B.C. A method was required for counting quantities larger than, say, what we can count on our hands. Roman numbers take seven letters and work them into a multitude of combinations to create small and large numbers. You'll notice that the letters can be written as capital letters (XVI) or lowercase letters (xvi).
The Seven Base Roman Numerals
There are seven letters that, when combined in various forms, create new numbers. Here they are, from smallest to largest:
Roman Numerals 
I = 1  C = 100 
V = 5  D = 500 
X = 10  M = 1000 
L = 50  
You can use a Roman numerals chart or conversion table to look up Roman numerals. Alternatively, you can easily learn how to calculate them yourself with a few simple rules.
Understanding Roman Numerals
Now we know that Roman numerals consist of a combination of the letters I, V, X, L, C, D, and M. The position of the letters in relationship to each other is what determines the value of the actual Roman numeral. For example:

If smaller numbers follow larger numbers, the numbers are added. For example, the Roman numeral XII calls for the addition of ten, one, and one. This results in the value of twelve: XII = 10 + 1 + 1 = 12.

If a smaller number precedes a larger number, the smaller number is subtracted from the larger. For example, the Roman numeral IV calls for the subtraction of one from five. This results in the value of four: IV = 5  1 = 4.
It's important to note how letters can be grouped. You might see III, which means three. Alternatively, you might see XXX, which equals thirty. The groupings are arranged from largest to smallest. Let's take a look:
How to Translate Roman Numerals
In order to break down a longer number like MCMLXXXIV into parts, consider this:

M is for the "thousands" (1000).

CM is for the "hundreds" (1000100 = 900).

LXXX is for the "tens," consisting of an L for 50 and XXX for 30 (10+10+10), adding up to 80.

IV is for the "ones" (5  1 = 4).
This gives us 1000 + 900 + 80 + 4, or 1984.
Additional Rules for Roman Numbers
Roman numerals don't use four identical letters in a row. So, you'd never exceed XXX, or 10+10+10, for the "tens" placement. Since we can't use four identical numerals in a row, 40 would not be XXXX but, rather, XL. Remember, X is for 10 and L is for 50; and when the smaller numeral comes before the larger numeral, that quantity is subtracted. In other words, 40 is represented and translated as 10 subtracted from 50.
Also, very large numbers can be written by adding a line atop the numeral. Anytime you see a line, that indicates the number should be multiplied by a thousand. So, if V has a line placed atop, that indicates 5 x 1000 = 5000.
Roman Numerals for Years
Let's see a few more examples of large numbers, as would be the case when representing a year:
 MCMXCIV = 1994. Watch how we advanced from 1984 to 1994. The LXXX (80) became XC (90). So, now we have M for 1000, CM for 100, XC for 90 (100 minus 10), and IV for 4.
It can be helpful to remember that we need to treat each "part" of the number separately (ones, tens, hundreds, etc.). So, even though 1999 is one fewer than 2000, you can't write MIM. The larger the numbers get, the more we must examine the parts that stack up to make the whole.

MDCCLXXVI = 1776. The Declaration of Independence was signed on July 4, 1776. Here, we have M for 1000, D for 500, CC for 200, L for 50, XX for 20, V for 5, and I for 1. Add those all up and you have 1776.

MCDXCII = 1492. Christopher Columbus sailed the ocean blue in 1492 and discovered America. This makes MCDXCII an important year. We can discern that breaking it down: M = 1,000; CD = 400 (500  100); XC = 90 (100  10); and II = 2 (1 +1).

MMX = 2010. Now, let's have fun and look at something a little more straightforward. MMX is short and sweet: M = 1,000, M = 1,000, and X = 10. That's 2010!
Roman Numeral Table
The table below can come in handy as you're familiarizing yourself with Roman numerals. If you commit as many of them to memory as possible, you'll immediately recognize how they stack up and can be used to represent any kind of number.
Table of Roman Numerals 
1  I  14  XIV  27  XXVII  150  CL 
2  II  15  XV  28  XXVIII  200  CC 
3  III  16  XVI  29  XXIX  300  CCC 
4  IV  17  XVII  30  XXX  400  CD 
5  V  18  XVIII  31  XXXI  500  D 
6  VI  19  XIX  40  XL  600  DC 
7  VII  20  XX  50  L  700  DCC 
8  VIII  21  XXI  60  LX  800  DCCC 
9  IX  22  XXII  70  LXX  900  CM 
10  X  23  XXIII  80  LXXX  1000  M 
11  XI  24  XXIV  90  XC  1600  MDC 
12  XII  25  XXV  100  C  1700  MDCC 
13  XIII  26  XXVI  101  CI  1900  MCM 
A Brief History of Roman Numerals
Roman numerals, as the name suggests, originated in ancient Rome. No one is sure exactly when Roman numerals came into use, but historians believe that the earliest time Roman numerals were used was somewhere between 900 and 800 B.C. This counting system is commonly thought to have started with the ancient Etruscans.
The symbol for one in the Roman numbering system represents a single tally mark of the kind people would notch into wood or dirt to keep track of items or events they were counting.
With these "notches," things could become complicated. Especially for trading, there was a need for a common method of counting. One could use their fingers, but what happens after 10? Actually, the fingers were the basis of this simple system.
The Roman numeral for one is a single line, just like one finger. The Roman number for five is V. This stems from the fact that when all five of our fingers are spread, there's a common Vshape between the thumb and the index finger. X represents ten because, if both hands are expanded, an X can be created when the two Vs merge, at the tips of our index fingers.
Roman Numerals in Modern Times
Roman numerals are still used today in a variety of applications. For example:

In outlines for a story or report.

On clocks and watch faces, such as IV for the number 4.

In books to number prefaces, forewords, and chapters.

On films and big events, such as Rocky II and Super Bowl XLVI.

For monarchs, such as Elizabeth II and Felipe VI.

For Roman Catholic popes, such as Pope John Paul II and Pope Benedict XVI.
History in Math
Isn't it fascinating to know that we still use a number system that possibly dates back as far as 800 B.C.? And, it's an interesting system, even if it takes some addition and subtraction to get where you're going and decipher what you're reading.
The next time you're formatting an essay for school and are required to use Roman numerals, say in the table of contents, you'll know you're enjoying a little bit of history in math.