A long, winding strip of cloth, usually thick cotton, wrapped tightly around the midriff up to the chest. Historically, samurai wore them under their kimono to resist injury.
In anime series, particularly in classic older ones, a delinquent character will be seen wearing one under their coat or unbuttoned shirt. The wrapping was a visible cue as to their general level of bad-assery. In this form the sarashi is wound mostly around the abdomen.
Alternatively, a tomboyish girl may wear one to bind and/or flatten her breasts, especially if she is trying to pass as male. This gradually evolved into what is nowadays the more common way of wearing a sarashi, which is in the style of a tube top; in this case, it wraps around only the chest area in a very nontraditional way, leaving the midriff bare (e.g. post #4296298, post #4076845, post #3616420, post #2644312). This sarashi style is especially seen on kendo girls and other fighters.