An excursion is taken more for pleasure than for practical reasons. Your business trip, when you spent most of the week waiting in airports and adjusting to different time zones, does not count as an excursion.
The Latin root for excursion is excurrere, meaning "to run out." So if you run out for a bit to get some fresh air, you've gone on an excursion. If you leave specifically to buy milk from the corner store and end up swimming in a stream, you've probably taken an excursion into the woods.