Burn wounds happen when the skin becomes too hot or too cold. This means that if you touch something in a freezer that is -80°C, you can burn your hand just as if you would touch boiling water. Because temperatures so low that you would burn yourself are very rare in nature, they were not recognized as burns until relatively recently and we associate burns with high temperatures.
There are several degrees that you can get burnt.

First degree burns barely damage your skin, but functions of your skin start getting affected and the skin can dry out. In response the skin gets swollen and can start to itch or even become painful.

Superficial second degree burns damage the top layer of the skin, the epidermis (See figure 1). In this part of the skin, there are no blood vessels or nerves. Blood still flows through the skin, and you still feel pain in the burnt skin. Superficial second-degree burns do not damage the basal lamina. The skin regenerates from the basal lamina upward.

Deep second degree burns go down to the middle layer of the skin, the dermis (See figure 1). The dermis contains nerves and blood vessels. Deep second degree burns partially damage the basal lamina. Thus nerves, blood vessels and the regenerating part of the skin are damaged. The sense of touch is lost in the burn, the skin loses fluid through blood loss and regeneration is slowed.

Third degree burns go all the way to the subcutan tissue (See figure 1). The basal lamina is lost, and regeneration is not possible except for the edges of the wound where there still is some basal lamina.

Fourth degree burns go furter down into muscles and organs.

Figure 3: The skin has four layers. The subcutan tissue lies between the skin and muscles in your body. The basal lamina forms the basis of the skin. The dermis contains many live cells and many nerve endings, hair follicles and glands suchas sweat glands. The epidermis is made of mostly dead cells and forms a protective layer all around your body.