Simply put, the vintage is the year the grapes for that particular wine were picked. Grapes are harvested only once a year after a meticulous and volatile growing process. In the Northern Hemisphere, this happens between August and November depending on the climate of that area. The warmer the area, the earlier the grapes will ripen and need to be picked. In the Southern Hemisphere the harvest months are between February and April.
Once the grapes are picked the winemaking process starts. Winemaking is the period from raw grapes to sealing the bottle with a cork, and many decisions in between. It can be a science for some and for others it's a mysterious process yielding distinct and delicious results, much like a cook may precisely follow a recipe or a chef may weave a perfect meal from instinct and gut.
As for the science, winemaking differs depending on the grape being used as well as the traditions and laws of the region. Many regions require a strict aging requirement in order for that region to be promoted on a label. The process always starts with fermentation and then goes into the barrel aging process. This process can be done in a matter of weeks or in some rare cases decades. Most wines are made within a 2 year period from when the grapes were picked. The winemaker ferments the juice of the grapes and then stores them in some vessel of choice. Oak barrels being the most commonly recognized for red, while white wines are often made efficiently in order to preserve the freshness of the thirst quenching nature of the majority of white wines.