scrub (v.) Look up scrub at Dictionary.com
"rub hard," c.1300, perhaps from Middle Dutch or Middle Low German schrubben "to scrub," or from an unrecorded Old English cognate, or from a Scandinavian source (cf. Danish skrubbe "to scrub"), probably ultimately from some cognate of shrub, used as a cleaning tool (cf. the evolution of broom, brush (n.1)).

Meaning "to cancel" is attested from 1828 (popularized during World War II with reference to flights), probably from notion of "to rub out, erase." Related: Scrubbed; scrubbing. The noun meaning "act of scrubbing" is recorded from 1620s.
scrub (n.) Look up scrub at Dictionary.com
"brush, shrubs," late 14c., "low, stunted tree," variant of shrobbe (see shrub), perhaps influenced by a Scandinavian word (cf. Danish dialectal skrub "a stunted tree, brushwood"). Collective sense is attested from 1805. Transferred sense of "mean, insignificant fellow" is from 1580s; U.S. sports meaning "athlete not on the varsity team" is recorded from 1892.