A hope chest is based on older cultural ideas and expectations. It was a chest or trunk for a young woman to collect the things she'd need to start off a household -- in "hope" of marriage and starting her own home. After that use, it would be used for storage. Sometimes it is used for regular storage, and sometimes for special, sentimental mementos. Hope chests are often lined with cedar making them a good place to store linens.
Hope chests often have sentimental associations and may be passed from generation to generation. An old tradition was to use it to collect the things a young woman would need to start her own household. And once that household was started, the chest could serve practical purposes, but it often was used to save precious mementos, such as a baby's Christening gown, a wedding dress, a quilt made by a beloved relative, love letters or other items needing protection from the elements and pests.
- Wikipedia's article on hope chest