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Roman numerals are numbers expressed by using letters of the Roman alphabet. Here's a mnemonic rhyme written by Peter Hobbs that explains the 7 basic roman numerals (I, V, X, L, C, D and M):

M's "mille" (or 1000 said)
D's half (500 - quickly read!)
C's just a 100 (century!)
and L is half again - 50!
So all that's left is X and V
(or 10 and 5) - and I - easy!

Thus M D C I I I = 1603
(or 1000 + 500 + 100 + 1 + 1 + 1)
and
D C C L X X V = 775
(or 500 + 100 + 100 + 50 + 10 + 10 +5)

Many people are familiar with reading I, V and X from clockfaces and just have trouble with the "higher" numerals. Here's an established acronym for just the four high ones (in ascending order):

"Lucy Can't Drink Milk"
(L,C,D,M - 50, 100, 500 and 1000)

The numeral "I" began as a finger-digit, while "V" represented the simplified outline of a hand (like a thumb and five closed fingers), this being clearer to write than five "IIIII" digits. In the same way the "X" represented two hands (ie. two V's mirrored), or ten. Later the Romans also used combinations of "one less than the next-highest numeral" for figures such as 9 (ie. "IX" rather than "VIIII"). An old established rhyme summarises how to read such combinations:

When "left" is small and "right" is bigger,
Subtract the "left" from "right-hand" figure.

Thus M C M L I X = 1959
(M+CM+L+IX = 1000 +[1000-100] +50 +[10-1])

Lastly, here's a popular and interesting pub quiz question. What number do you get if you add up all of the Roman numerals?

M D C L X V I = 1666
(or 1000 + 500 + 100 + 50 + 10 + 5 +1)
which just happens to be the year of the Great Fire of London!