The tally (or tallow) lamp was used by miners when underground. It worked by being filled with animal fats or oils, then the textile wick was pushed into the spout. The wick was lit and would burn, using the oil to stay alight, very similar to a much earlier Roman oil lamp. The hook on the side of the lamp was used to put it onto a jacket, hat or piece of wood underground. It would not have provided much light to miners, but at that time, was about the only method of light available. As the lamp had an open flame, it could only be used in place underground where it was known that there weren't dangerous gases.
To us today it looks like quite a cute little light, which is small, well-made and reminds us of a teapot! However, to miners, it would have been their only source of light in the pitch darkness, could have been potentially very dangerous and was a regular staple of life underground around 1900.