In most cases, we can deliver within 3 days, excluding holidays.
Literal
Holidays [object-を] excluding 3-days within [at-に] deliver-can cases [subject-が] most is.
A standard shipping policy statement. ~を除き (excluding) is a formal way to mark exceptions. お届けできる uses the honorific お prefix with the potential form — polite customer-facing language. ケース (case) is a loanword. ほとんど (most/almost all) quantifies the reliability.