I used to have in my home a big Wolf stove with a salamander. It is a wonderful machine for broiling, but it is big, heavy, expensive, and throws a lot of heat into the room. It doesn't have a door like an oven door. If you are considering one for your home, I emphatically recommend that you go where you can see one in action. I'd say it really isn't appropriate for most home kitchens.
A Salamander is a very short (in vertical dimension) oven that is used for super high heat broiling...think a home broiler on steroids. Restaurant salamanders are quite long, to allow for many dishes to be blasted with heat at a time, melting cheese, creating crusts, etc.
There are home versions, I know Viking makes one, that aren't as long. Martha Stewart had one such example on one of her many sets over the years, and I recently saw a similar model in an interview with Jeffrey Steingarten on Food Network.
Actually looked this up a week ago. It is most commonly a machine which grills, but traditionally it's a branding iron used to caramelize sugar, like on creme brulee. I think you can still buy the terracotta dishes used for crema catalana (Spanish equivalent of creme caramel) which come with a salamander which fits the dish perfectly.
I first saw one on 'sugar rush' on the food network, on a piece on Lady M patisseries. They use it on their crepe cake. Very impressive. One swipe, and the sugar caramelized and hardened.