I've seen finishes (and finishing techniques) described as providing a lot of "luster". I can understand matte, which is similar to satin, and that sheen is akin to gloss. But what do people mean when something has a lot of "luster"?
Let me preface my comment by saying that quite a bit of the terminology used in woodworking is used loosely or informally, so one person's understanding of and use of a word may not match another person's precisely.
As far back as I can remember knowing it, lustre in this context was used merely as another word for shine (this is in British English). Dictionary.com's listing for the word notes that it is chiefly British and gives as the first definition: 1. reflected light; sheen; gloss.
I can understand matte, which is similar to satin
In the coatings industry satin would normally mean a sheen level somewhere between matt and gloss. Matt and satin gloss levels do vary from one product to another however, meaning it possible to find a matt varnish from one manufacturer and a satin varnish from another that have approximately the same gloss.
Note since this keeps on getting 'corrected': matte (American English) = matt (British English).
luster is the sheen and clarity which adds depth as well as shine showing the beauty of the wood species.
Luster is the amount of particulate matter imbedded in the finish. Often the particles are silica. The more particulate matter, the more the appearance of the wood is dulled by light scattered from the intervening particulate matter. The highest luster, often called gloss or bright, has no particulate matter in the finish.
Luster (lustre for the British) has many uses. In reference to wood, it refers to the reflective quality of the grain of the wood. You may have noticed that a nicely figured piece of wood will look different as the light hits it from different angles or as you walk around a piece. I have heard people refer to this as 'the wood looking alive'. Opaque finished will mask this reflective quality and transparent finishes will make it easier to see (so would wetting the wood, but that is less permanent). Some stains will enhance the contrast between the reflecting wood and the rest.