Cross-border describes something that happens across the line between two countries — money, people, trade, crime, phone calls, pollution — anything that starts on one side and ends up on the other. It sits in front of a noun almost all the time: cross-border trade, cross-border payments, cross-border crime, a cross-border attack. You will meet it most in news and business writing; it is a slightly formal word, and nobody says it about their own weekend trip. If you drove to another country to buy cheap milk, you would say "I went across the border", not "I made a cross-border journey" — though a newspaper writing about a thousand people doing the same thing would call it cross-border shopping. That is the pattern: it likes big, repeated, official-sounding movement more than one person's day out. It can also work as an adverb, as in "the goods move cross-border without tax", but that use is rarer and belongs mostly to trade and banking writing; in ordinary sentences people say "across the border" instead. One more thing worth noticing: "border" here is a national border. Talking about two counties or two cities inside one country, English usually says something else.