Typically a portion of the contents of the last barrel are removed and bottled. Then the last barrel is filled from the next-to-last barrel, etc., until the first barrel is filled with new wine. The barrels are then left to age until the process is repeated. A solera can easily be the largest capital investment of a family firm, and is typically passed down to one's descendants.
Wine produced from a solera cannot have a vintage date because it is the product of wines from many years. The last barrel has at least a tiny (albeit usually insignificant) fraction of the first wine ever put in it, which could be hundreds of years old. However, if the movement of wine is slow enough, it is possible to establish a minimum age of the blend. For example, if one has ten barrels, and transfers wine along once a year, the result is a minimum of ten years old, and can be labeled as such. However, the average age is older than that.
The solera system is abused in the case of balsamic vinegar, because the labeling laws permit vinegar to be labeled with the age of the oldest vinegar in the blend. Not surprisingly, producers take a tiny cask of 12-year-old vinegar, blend it with a huge amount of new vinegar, and label the result "12-year-old vinegar". In the case of the much more strictly controlled and much more expensive aceto balsamico tradizionale this is not permitted.