Stuck or sunk into mud, wetland, or a difficult situation from which escape is hard.
From 'bog' (from Irish 'bogach' meaning soft/marshy), becoming a verb in English by the 16th century. It originally described getting stuck in actual bog, then evolved to figurative uses.
When you're 'bogged down' in work or problems, it's because real bogs are literally places where you sink and struggle—the word's history is about actual people getting trapped in Irish and Scottish marshes.
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