Anything offshore happens out at sea — and when you're talking about the wind, offshore means it's blowing toward the land.
During your Caribbean vacation, you might paddle out to an offshore sandbar, a raised area away from the beach. You could also put on fins and a snorkel and check out some offshore coral reefs. Offshore breezes bring cooler air to the coast, and offshore drilling is a method of seeking out underwater oil and gas. If someone has an "offshore bank account," it means they keep their money in a foreign country — probably to avoid paying taxes on it.