Padding in the tongue and around the ankle helps provide comfort and support. Your boot should come up to at least your ankle or a bit higher to provide you with adequate support on rough trails or other uneven terrain. Your ankles are inherently unstable, and can use the help, especially when you are carrying a heavy pack. There are some other considerations, such as the idea that an above-ankle boot also helps keep mud or snow from trickling in to make your day uncomfortable. Your boot should have as few seams as possible.
Seams are also the most likely areas for boots to come apart with heavy use.
While not exactly essential, inserts can make the difference between comfort and agony if your feet are hard to fit. You can use inserts to fine-tune a boot's fit and make your hiking life more enjoyable. A deeply lugged sole provides you with good traction. Many boot manufacturers have their own preferred design, while some use soles provided by companies that design high-quality soles, but don't make boots. Hard synthetics may not be a good option, depending on the manufacturer.