To make something green in color or to cover with green growth or vegetation.
From be- (prefix) + green (from Old English grene, related to 'grow' and Germanic roots meaning 'to flourish'). Green was originally named for its association with growing things.
The word 'green' is actually connected to 'grow'—they share the same root because early languages named the color after what it represented: plants and life. So to 'begreen' something is to literally restore it to growth and vitality.
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