LDraw unit
The LDraw unit (or LDU) is the basic unit of measure in the LDraw parts library. Since LEGO elements do not have exact english or metric measurements the LDU is expressed in terms of elements. The rectangular prism part of a 1x1 brick (not including the top stud) is 20 wide x 20 long x 24 high in LDU.
Some unofficial measurements
Some AFOLs are also used to talk in term of fraction of "stud" where a "stud" is the horizontal size of one size of a 1x1 plate or brick. This can lead to confusion as the diameter of a stud is 0.6 "stud".
1 "studs" = ~8 millimetres^{1} (~5/16 inches) = 20 LDU ("~" means "approximately")
Others will use "brick" in this same place. Hence ... when talking about parts, LDU should be prefered as it allows to deal with whole numbers and not fractions, and doesn't lead to confusion with any idiomatic vocabulary.
1  20 LDU is very close to, but not exactly, 8 millimetres. It is believed this is due to molding tolerances and draft.
Conversion Table

To the left is a table with conversion factors among
 LDU (LDraw Units)
 "studs" (stud units as described above)
 "bricks" (brick units as described above)
 "plates" (plate units as described above)
 cm (centimetre, Metric)
 in (inch, US or Imperial)
 pt (point, printing measure)
It should be read as row in column, e.g. 1 LDU(row) = 0.04 cm (0.04 is value of cm column) whereas 1 cm (row) = 25 LDU (25 is value of LDU column)
External Links
 Ldraw.org LDraw.org article on LDU
 LEGO Dimensions diagram
 Dave Eaton's LEGO Scale Converter