The difference between wreath and wreathe is similar to that between breath and breathe as well as sheath and sheathe. Wreath is a noun, and wreathe is its corresponding verb, meaning (1) to twist or entwine into a wreathe, or (2) to decorate with or as with a wreath. So, for instance, during the holiday season, one might festively wreathe a tree with wreaths.
Examples
Wreath
That could be why every January, I get a certain sugar craving that can only be satisfied by an icing-drenched, cinnamon-laced braided wreath. [Washington Post]
I discovered old photographs of her dressed as Mother Earth, wrapped in a bed sheet with a plastic Christmas wreath on her head. [Guardian]
The Lincoln Association of Jersey City will lay a wreath tomorrow afternoon and later host a dinner in honor of the 16th president’s birthday. [NJ.com]
Wreathe
The mysteries of high finance now wreathe their enigmas around Ibrox and Tynecastle. [Scotsman]
My support for Ireland dissolved when this brouhaha began, when the politicians got involved, when they began to wreathe themselves in the luxury of perpetual victimhood. [Times Online]
Mass graves wreathe this ancient Afghan city, bearing the grim evidence of its central role in this country’s civil war. [New York Times]