To bring people together for a meeting or to come together as a group for a formal purpose. It is often used for official gatherings like committees, courts, or conferences.
From Latin *convenire* 'to come together, assemble', from *con-* 'together' and *venire* 'to come'. It entered English through French and kept its sense of formal gathering.
Convene is like 'come together' wearing a suit and tie—it sounds official. Parliaments, courts, and councils convene; your friends usually just 'meet up.' The same Latin root also gave us 'convenient' and 'convention,' all about coming together in some way.
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