A bralette is an undergarment for the upper body less structured than a bra but much briefer than a camisole. This early pre-decessor of the bra was popular in the 1910s and 1920s. In the 1920s the pre-bra morphed from the cropped camisole look to the bra look, but the bras of the time were really just wisps of silk with no support. 

In modern times, the bra options include this unstructured style, and bralette has come to mean any skimpy undergarment which covers the breasts but does not add support.

Edwardian - early 1920s bralette

Mid 1920s- early 1930s bralette