In or towards the United States — said by Americans who are somewhere else. That last part is the whole point of the word. It carries a feeling of looking back home across the ocean, so it is used mostly by American soldiers posted abroad, and by Americans living or travelling overseas. A soldier in Germany says "I fly stateside next month" or "my family is stateside". It works two ways in a sentence. As an adverb it means to or in the US and needs no preposition: go stateside, back stateside, ship it stateside. As an adjective it sits in front of a noun: a stateside address, stateside prices, my stateside phone number. The capital letter is optional — stateside and Stateside are both common. The tone is relaxed and slightly military; you would not write it in a formal report, where you would just write "in the United States". Though actually, outside American mouths the word sounds odd. If a Taiwanese student who has never lived in the US says "I'm going stateside", it will sound like a line borrowed from a film. Understand it when you hear it; you rarely need to say it.