There are a lot of factors that determine how well (long) a particular wine will age.
At The Wine maker's Toy Store, George generally states how long a kit wine should age before drinking and how long the wine can age and still stay good.
A wine starts out not tasting as well as it will when fully matured (the sweet spot). And, once fully matured, it will stay that way for a reasonable time before it finally starts "going down hill" as it gets older.
A wine will last longer if it has sugar; the more sugar, the longer it will last (generally speaking). There are very sweet Rieslings that can last 100 years. That's a long, long time, especially for a white wine.
Another factor that determines the aging ability is acid content.
Still another is the total dissolved solids (TDS) in the wine. The more the TDS, the longer the wine can age.
One factor to consider about wines that age longer is that the longer a wine can age, the longer it takes for that wine to mature. It will taste rough and tart for a much longer time before it smooths out (matures). This factor and the lower TDS in most dry white wines is why they are drinkable sooner, but typically won't age as long.
The lower priced red wine kits tend to have less TDS, so they mature faster, but won't last as long as a premium red kit, which has a juicy grape pack, which of course is loaded with TDS. With a premium grape pack kit, we sometimes have to wait 2 years or more before it matures. (This is the reason why I keep saying that if you can't stay out of the wine until it matures, you should buy and make the lower priced kits, which mature quicker.)
I have read that for a true Italian Barolo, you should not buy the wine until it is at least 10 years old, then you should let it age for at least 10 more years before you drink it.