A person who drives a taxi or cab for a living; a taxi driver.
From cab plus the agent noun suffix '-er' (one who performs the action), following the standard English pattern for naming people by their occupation or what they operate.
A cabber needs to know not just how to drive but where everything is in the city—before GPS, London cabbers had to memorize thousands of streets in a test called 'The Knowledge,' which actually increased the size of their hippocampus (the memory part of the brain), so geography was literally reshaping their brains.
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