US tax law sorts non-citizens into resident aliens (taxed like citizens, on worldwide income) and non-resident aliens (taxed only on US-source income). You're generally a resident alien if you hold a green card or meet the Substantial Presence Test based on days in the US; otherwise you're a non-resident alien.
The distinction drives what the US can tax and which forms you file. It matters not just to immigrants in the US, but to anyone weighing how time spent in the US would affect their tax status.
Why it matters for your move
If your move involves the US — leaving it, or spending meaningful time there — whether you're a resident or non-resident alien shapes your entire US tax exposure.