Motoring is driving a car, thought of as an activity or a subject rather than as one trip. It is a British word, and an old-fashioned one — it comes from the days when owning a car was still a pleasure and an adventure, and going out for a drive in the countryside was the whole point of the afternoon. Because of that history, it survives best in fixed phrases: a motoring holiday, a motoring magazine, motoring offences (traffic offences, in a court), the motoring public, a motoring correspondent on a newspaper. Nobody today says 'I was motoring to work' unless they are joking or being posh. For ordinary driving, English says driving: 'I drove to Taipei', not 'I motored to Taipei'. There is one other use worth knowing, informal and British: 'motoring' can mean going along fast and smoothly, or making great progress. 'By half-time they were really motoring' means the team had got going and was doing well. That use has nothing to do with cars any more — it just borrows the picture of an engine running strongly.