Gewürztraminer is a variation of the Traminer grape meaning 'of the village of Tramin', 'Termeno' in the Alto Adige in the far north of Italy where it was popular between the 11th and 16th centuries. It is a variation of the distinct and ancient Muscat grape.
The name Gewurz is curious in that, although its German translation means 'spicy' - in fact the official protected name only occurred in 1973, it's French and Italian names (traminer-musque, traminer-parfume, and termener-aromatico) lead one to believe that the wine's perfumes would indicate a more accurate translation. Roses, flowers and Turkish-delight are generally the most common aromas, followed by lychee's and even grapefruit. Plus cloves and nutmeg are also noted, thus the spice references.

 

Differences could be attributed to the terroir, except that the one characteristic of this grape family is that they give their intense flavour to the wine independent of where they are grown.
A better answer might lie in climate; a cooler climate with a long, slow ripening season seems to produce the superior expressions of this wine. Perhaps the Germans felt, at the start of the Gewürztraminer renaissance in Alsace in the late 19th century, their words for aroma and perfume, being taken from the French, did not suit their patriotic pride.
One could also speculate that the fact that Gewürztraminer is very often suggested as a compliment to spicy foods (Asian and Latin American) or sausages, pork and sauerkraut - could have influenced its name.
Gewürztraminer wine can be dry to very sweet and is known for its high alcohol, low acidity and golden colour. It is a powerful wine that likes powerful foods. It can also be used as a dessert wine or to accompany rich cheese such as Munster. Interestingly, the cheese is commonly served with bowls of caraway, cumin or fennel seeds which are sprinkled on the cheese as you eat it.
The more one learns about Alsace, the more one understands why they might name their wine 'Spicy Tramin'.