Maybe it is a British thing, we say it quite frequently. It is fairly informal. It means a week from Tuesday (so not the coming Tuesday, the one after that).

Hi there. "Tuesday week" means not the next Tuesday, but a week from next Tuesday. For example, today is Monday 16th, next Monday is the 23rd, Monday week is the 30th. Hope it helps you.

Next Tuesday.

It litteraly means that on one of those Tuesdays your going to eat tacos, so prepare your belly for a feast)

I have never heard this phrase either, Tuesday week? ??? Hmmm usually it's just this Tuesday, or next Tuesday here in the states.