The short answer is vintage is the year the grapes were harvested, and its important because in some regions it can determine if the wine is good, bad or just plain ugly.
The long answer is a vintage wine is one made from grapes that were all, harvested in a single specified year. In certain wines, it can denote quality, as in Port wine or Champagne, where Port or Champagne houses make and declare vintage Port or Champagne in their best years. They then only use grapes harvested in those years to produce their vintage wine, normally their house style is made by blending wine to get the flavours they want.
The importance of vintage is disputed these days with certain commentators suggesting that all our advancement in modern technology it allows the wine maker to create good wines in bad years. Also in many wine producing regions, particularly in the New World the conditions in which the grapes are grown are not subject to as wide a variation in conditions as Bordeaux or Burgundy in France say. As a result vintage is more important in these region than it would be in say the Barossa valley in Australia. That is not to say that they can’t have great vintages and growing years in Australia, just that they are less likely to have bad ones. Or that the french don’t cheat a bit like adding a bit of sugar to under-ripe grapes to get the alcohol level up!