Spicy foods contain a chemical called capsaicin, which activates a receptor found in your mouth and on your tongue called a TRPV1 receptor. There is some variation in the sensitivity of these receptors, and even the amount of them, from person to person. This variance may be one reason some of us can’t handle the spice, and others love it. Studies have shown that repeated exposure to capsaicin raises the amount needed for a similar effect, so it may also be that the more spicy food you eat, the more you can handle. Lastly, there is likely a psychological element at play in spice-lover's obsession- studies have shown that many spice enjoyers do feel the burn like spice haters, but find it a pleasurable experience, rather than a painful one. Indeed, it seems that to love spicy food is to take pleasure from the pain.
The reason why we feel the burn differently is both physical and psychological.