For firefly luciferase, at least, it catalyzes, in the presence of Mg2+, the reaction:
luciferin + ATP + O2 => oxyluciferin + AMP + PPi + CO2 + light
Luciferase is now widely used as a research tool for determining promoter function, i.e. whether a gene get's turned on or not.
Let's say I want to determine what and how the TNF-alpha gene in macrophages responds when I add lipopolysaccharide to them.
I would transfect my macrophages with a reporter construct, a piece of DNA that has the promoter from the TNF-alpha gene. The promoter is the control element of a gene, the part that is involved in the turning on and off of the gene, and not the product of the gene itself. Except in my reporter construct, this TNF-alpha promoter would be controlling the expression of luciferase, instead of TNF-alpha.
Then, I would treat my transfected macrophages with with varying amounts of lipopolysaccharide. The TNF-alpha promoter would get turned on to various degrees. After a set time, I can determine how and if the TNF-alpha promoter responded by determining the amount of luciferase made by the cells (using a luminometer).
This is just an example, of course, you could replace the TNF-alpha promoter with any other natural or artificial promoter, and replace the macrophage with any cell you want to study, and replace the lipopolysaccharide with any stimulus you with to use.
As an additional note, GFP is a totally different kind of protein, and luciferase itself isn't really fluorescent.
Luciferase is an enzyme which uses energy to give off light. GFP, like other fluorescent molecules, just gives off light when excited by light. Basically, if you shine a certain wavelength light at GFP, it emits light at another wavelength.
GFP is still really cool, though.