Triage borrows its name from emergency rooms: look at everything quickly, then decide the order. For email the usual buckets are reply now, reply later, hand over (escalation), and ignore or archive.
Why it matters
Without triage, the loudest or newest email gets answered first and a quiet but urgent one sits at the bottom. Most of the mail in a support inbox is not a customer question at all: order confirmations, tool notifications, mailing lists. Clearing those out first makes the real work visible.
An example
On Monday morning the inbox holds forty emails. Twelve are shipping notifications, five are newsletters, one is an invoice from a supplier, and the rest are customers. Triage leaves twenty-two customer emails, with the two about a failed payment at the top.
In ReplyPen: Newsletters, notifications, receipts, auto-replies, internal mail and spam get no Draft automatically, and a Rule can skip or always draft email by sender, domain, subject or body text.