A heat-moldable liner is a foam liner that can be warmed up in a shop and shaped to your foot's specific contours. Instead of spending days or weeks breaking in stiff boots, a shop tech heats the liners and you wear them while they cool, giving you a custom fit right out of the box.
The biggest benefit is heel hold—when the foam forms around your ankle and heel, it locks your foot in place, which means less lifting and better control on turns. It also reduces hot spots and pressure points that can make a day on the mountain miserable.
If you're riding more than a few days a season, heat-moldable liners are absolutely worth it. Most mid-range and higher boots include them now. Just make sure you actually get them molded at the shop when you buy—skipping that step defeats the whole purpose.