Flex refers to a rating that tells you how hard it is to flex the boot forward. Aggressive or heavier skiers often prefer super-stiff boots (120-130+ flex rating) to handle high speeds and challenging terrain. Intermediate skiers may want a boot with a flex around 100-110, and beginners, smaller skiers, and park skiers might prefer a softer boot in the 80-100 range.
Last width refers to the width of the toebox of a ski boot. The width of your foot dictates the last width you need to achieve the right balance of performance and comfort. Expert skiers with wide feet may opt for a narrower last width, sacrificing some comfort to obtain the response of a close-fitting boot. Others may choose the all-day comfort of a wider last.
Many alpine boots now include features that make them more more useful for backcountry skiing. A 'walk mode' switch makes bootpacking easier on your ankle and foot. Some boots use aggressive rubber soles, or accept add-on rubber soles, that make it safer to keep your footing in technical terrain.
Boots also feature canting or forward lean adjustments, buckles configuration and their degree of adjustability. Thermoformable liners, which can be customized to match the shape of your foot, are fairly standard on higher-end boots.