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EXP describes the distance over which an object becomes opaque as a ray passes through it. Zero is a special case; when set to zero, translucency is not evaluated (the object is perfectly clear if transparent.)
If you have a sphere of radius 1, then setting translucency to 2 (the distance of the diameter) is equivalent to saying that the sphere is opaque when viewed through the center, and more transparent towards the edges. You should keep in mind that when an object is translucent, but has a different index of refraction than the medium from which a ray enters and/or leaves it (EG, the atmosphere's IOR is 1.0 and the sphere's is 1.5) then the rays warp around inside the object and take longer paths, so the translucency of the object becomes a great deal more apparent.
Translucency has interesting effects inside objects that involve multiple internal reflections, such as a faceted gem. A significant amount of translucency will cause the gem to become darker along long reflective paths; the net result is typically that the edges appear clear and show the sparkle that one would expect, but that the deeper view into the gem darkens. This is exactly how most gems behave in real life — only the very finest of colored gems exhibit extreme clarity. This is why extremely clear rubies and emeralds can be worth more than diamonds by carat weight.
See also: Language elements <transparency> , <refraction> and <atmosphere>