It was originally known as The Museum of Manufacturers and contained collections on both applied art and science. The first director, Henry Cole, wanted the museum to be "a schoolroom for everyone" and education of the public was its mission. The museum was first located at Marlborough House, later moved to Somerset House, and finally transferred to South Kensignton where it still remains today. When it moved for the last time in 1857, it was renamed "South Kensignton Museum". The year after efforts were made to have the museum open at later hours so as to be accessible to the working classes by introducing gas lighting. It was renamed "The Victoria and Albert Museum" in 1899. Over the years, many additions have been built onto the museum and its collections are numerous and massive, being one of the largest museums in the world. It is largely an art gallery of many mediums including paintings, photographs, sculptures, tapestries, etc. The V&A has a combined collection of over 6.5 million objects, although not all of them are housed in the museum at the same time. 

Sources

https://www.vam.ac.uk/collections/the-va-story#intro

https://www.british-history.ac.uk/survey-london/vol38/pp248-256

https://en.wikipedia.org/wiki/Victoria_and_Albert_Museum