A bra that provides at best minimal support under the breasts, leaving the upper part and nipples exposed. As the name suggests, it is essentially a "shelf" to hold up the breasts.
Example: post #1143998
The term "shelf bra" may also refer to "built-in bras" that may be included in some garments, such as tank tops and swimsuits. This tag is only for the specific piece of lingerie and not for the feature built into garments.