The reactions that take place during the conditioning phase are primarily a function of the yeast. The vigorous primary stage is over, the majority of the wort sugars have been converted to alcohol, and a lot of the yeast cells are going dormant - but some are still active.
The Secondary Phase allows for the slow reduction of the remaining fermentables. The yeast have eaten most all of the easily fermentable sugars and now start to turn their attention elsewhere. The yeast start to work on the heavier sugars like maltotriose. Also, the yeast clean up some of the byproducts they produced during the fast-paced primary phase. But this stage has its dark side too.
Under some conditions, the yeast will also consume some of the compounds in the trub. The "fermentation" of these compounds can produce several off-flavors. In addition, the dormant yeast on the bottom of the fermentor begin excreting more amino and fatty acids. Leaving the post-primary beer on the trub and yeast cake for too long (more than about three weeks) will tend to result in soapy flavors becoming evident. Further, after very long times the yeast begin to die and break down - autolysis, which produces yeasty or rubbery/fatty/meaty flavors and aromas. For these reasons, it can be important to get the beer off of the trub and dormant yeast during the conditioning phase.
There has been a lot of controversy within the homebrewing community on the value of racking beers, particularly ales, to secondary fermentors. Many seasoned homebrewers have declared that there is no real taste benefit and that the dangers of contamination and the cost in additional time are not worth what little benefit there may be. While I will agree that for a new brewer's first, low gravity, pale beer that the risks probably outweigh the benefits; I have always argued that through careful transfer, secondary fermentation is beneficial to nearly all beer styles. But for now, I will advise new brewers to only use a single fermentor until they have gained some experience with racking and sanitation.
Leaving an ale beer in the primary fermentor for a total of 2-3 weeks (instead of just the one week most canned kits recommend), will provide time for the conditioning reactions and improve the beer. This extra time will also let more sediment settle out before bottling, resulting in a clearer beer and easier pouring. And, three weeks in the primary fermentor is usually not enough time for off-flavors to occur.