"The drive" is the journey by car that they are on at that moment.

Hi, The other commenters make good points, but I think the issue with that sentence is that it uses slang, and contractions. "... on the drive" is a short form to say "... on the drive towards home/drive towards the sports park/drive towards the destination". Another way of saying this would be that "He was talking for a long time while he was driving his car" "catting away" is a slang way of implying he was talking a lot, like a cat continuously making noises, like purring or meowing. He is talking a lot about his car. That is how I would interpret this sentence.

Hi Gyeonwon, He talked continuously throughout the drive about his car... You can't say 'almost continuously. Because it's either continuous or not. Hope it helped :-)

I suspect "catting away" is a typo, and the original was "chatting away". That would be a very common, idiomatic way of saying that he was talking a lot, and I've never once heard "catting away". Also, although "the drive" certainly could refer to the driveway, that doesn't ring true to me. I reckon it means the time they were in the car together, driving from one place to another. It doesn't necessarily imply he was driving at all. Also, I respectfully disagree with Francisco - "almost continuously" would be quite a common way of saying that he was talking a lot.

The sentence isn't very clear without context. It could mean "to talk whilst he's driving." However, to mean it suggests he is standing on the drive outside his house. He is chatting about his car parked in front of him. As I said, the sentence isn't very clear but drive as a noun usually means a place/private road outside your house. Hope this helps!