There are a lot of definitions for giclee on the internet but this one we can endorse;
Giclee is a term for the process of making fine art prints from a digital source using inkjet printing. The word "giclee" is derived from the French language word "le gicleur" meaning "nozzle", or more specifically "gicler" meaning "to squirt, spurt, or spray". It was coined in 1991 by Jack Duganne, a printmaker working in the field, to represent any inkjet-based digital print used as fine art. The intent of that name was to distinguish commonly known industrial "Iris proofs" from the type of fine art prints artists were producing on those same types of printers. The name was originally applied to fine art prints created on Iris printers in a process invented in the early 1990s but has since come to mean any high quality inkjet print and is often used in galleries and print shops to denote such prints.
From Wikipedia (with minor alteration); http://en.wikipedia.org/wiki/Gicl%C3%A9e
In truth the Iris was the first inkjet printer to produce continuous tone or near continuous tone prints. Even though it had a comparatively low resolution by today's standards of 300 dpi it had an innovative line screen that let it appear to have a resolution of 1800dpi. Given that the printer itself cost $75,000 Iris prints had snob appeal as well as technical superiority at the time. Here is an interesting article from 1987 extolling it's benefits.
Since then technology has moved on, the Iris only had 4 colors, today's inkjet have between 7 and 13, and the resolution now is closer to an actual 2880dpi than an apparent 1800dpi. Still the Iris retains it's appeal and some places will insist that if it's not an Iris print then it's not a giclee. We dont agree, giclee has become a standard term for a fine art inkjet print that can be produced on a wide range of materials from watercolor paper to canvas and as distinguished from a print made with a digital silver based process such as a Digital C print.
With attention being paid early on to the archival qualities of inkjet prints—we attended this 1998 conference at Cooper Union discussing the issue in regard to the collectability of inkjet prints by museums—the giclee became established as a viable means of printing with few or no drawbacks for the artist or collector.