A place where valuables are stored, especially the clothes, linen, etc., that a woman might store in preparation for her marriage. Literally, the lowest drawer of a chest of drawers.
The figurative use of the term 'bottom drawer' to refer to the items that a woman stores in readiness for marriage began in the 19th century. It was certainly in use in Cheshire by 1886, as this entry in Robert Holland's A glossary of words used in the county of Chester [Cheshire] shows:
"If a young woman were to buy a set of teathings, or a tablecloth, or what not, and were asked what use she had for such things, she would answer, 'Oh! they're to put in my bottom drawer.'"
It is odd that the similar phrase 'top drawer', which refers to items of the best quality and which also derives from a literal reference to the drawer of a cabinet, should be otherwise unrelated to 'bottom drawer'. We might imagine that if 'top drawer' is the best, then 'bottom drawer' would be the worst. It's not so, which amply demonstrates the difference between the literal and the metaphorical.