I would divide the idea of "secondary" and "aging" The term secondary tends to be used for non-carbonated beer in a non-serving vessel. A lot can be said on the topic but the gist is that pitching starters, quality sanitation, and good fermentation control reduce the stress on the yeast. Secondary was used to get the fermented beer off the yeast before they started to autolyse. With healthy yeast from good practices, we can leave the beer on the yeast cake longer, letting the remainder of the active yeast (still in solution, kept if you transferred to a secondary) metabolize fusel alcohols and diacetyl in the primary vessel. All that being said, there really is nothing wrong with a secondary and it may be needed if you are planning on dry hoping or adding other things such as fruit to your beer.
The term aging is broader and is typically used for complete beer ready to drink. There are two general types of good aging reactions. Tanins, polyphenols (small tanins...kinda), and other compounds will coagulate and fall out of the beer with time and generally improve flavor. This is best seen in dark, or complex beers with a lot of crystal and roast malt. These beers tend to be bigger so that's one way to generalize that bigger beers benefit from aging. The other way is directly related to high alcohol content beers. That is, fusel alcohols produced during fermentation of high gravity wort. These will undergo esterification reactions with time and become less perceptible thus improving a bigger beer as well.
If you're interested in the details see: How to Brew by Palmer (3rd ed.), Yeast by Zainascheff, or Principles of Brewing Science by Fix. Also, the Brewstrong podcasts with Palmer and JZ are helpful.