The two-day convention exists because settlement needs banking hours in both countries. Both currencies' financial centres must be open on the spot date, so a holiday in either one pushes it out. USD/CAD is the main exception and settles next business day, T+1, because New York and Toronto share a time zone.
The spot date sets the interest window. The interest-rate-differential you pay or earn covers the period from the current spot date to the next one, which is why a Wednesday roll spans three days: see triple-swap-wednesday.
Example: a EUR/USD trade dealt on Thursday 5 March settles Monday 9 March, because Saturday and Sunday are not business days. If Monday were a US holiday, it would move to Tuesday 10 March.
Related: value-date, spot-fx, rollover, triple-swap-wednesday