spruce (n.) Look up spruce at Dictionary.com
1660s, "evergreen tree, fir," from spruse (adj.) "made of spruce wood" (early 15c.), literally "from Prussia," from Spruce, Sprws (late 14c.), unexplained alterations of Pruce "Prussia," from an Old French form of Prussia.

Spruce seems to have been a generic term for commodities brought to England by Hanseatic merchants (especially beer, boards and wooden chests, and leather), and the tree thus was believed to be particular to Prussia, which for a time was figurative in England as a land of luxuries. Compare spruce (adj.). As a distinct species of fir, from 1731.
spruce (v.) Look up spruce at Dictionary.com
"to make trim or neat," 1590s, from spruce (adj.). Related: Spruced; sprucing.
spruce (adj.) Look up spruce at Dictionary.com
"neat, smart in dress and appearance, dapper, brisk," 1580s, from spruce leather (mid-15c.; see spruce (n.)), a type of leather imported from Prussia in the 1400s and 1500s which was used in England to make a popular style of jerkin that was considered smart-looking.