Even when the yeast are largely finished with the primary fermentation process, if left to work longer they will clean up a lot of their own by-products, usually resulting in a cleaner flavor. I also noticed that I often get an extra point or two drop in FG since I started leaving them in primary longer (compared to the same recipe done with a shorter primary). In addition, after a 2 week primary - 2 week secondary and 3 weeks bottle conditioning, 90% of my batches have lost their green flavor and are ready to drink.
I prefer to secondary most of my beers, but many folks on here skip the secondary and instead opt for a 3-4 week long primary. I started out using the 1-2-3 method but as my brewing progressed (and my pipeline built up) I increased my primary time to 10 days, then to 14 days and I'd definitely say my beer has improved.