What it means
A padded mailer, usually the bubble-lined sort, for posting stuff that needs a bit of cushioning so it doesn't get battered in transit. In the UK people say jiffy bag all the time even when it isn't the actual brand, same way people say Hoover for a vacuum. Dead ordinary bit of post office lingo, very British, very practical.
Usage examples
"Need to send your mate a phone case? Stick it in a jiffy bag, whack on loads of tape, and lob it in at the Post Office."
"I need to send my nephew his birthday Lego brick in Manchester this week, stuck it in a jiffy bag with extra tape around the corners, dropped it off at the post office in the village before lunch, and the lady at the counter sent it second class with two pretty stamps from the new collection."
"The eBay buyer from Glasgow demanded a refund because his vintage camera lens arrived in a flimsy jiffy bag rather than a hard cardboard box, the courier had clearly stood the parcel on the doorstep face down in the rain, and the insurance claim took three weeks of polite emails to resolve in the end."
"Chuck the necklace in a jiffy bag or it'll turn up looking like it's done ten rounds with Royal Mail."
"I've got three Vinted parcels to send, just need a couple of jiffy bags and I'm sorted."
Where it comes from
It comes from Jiffy, the UK packaging brand that made padded envelopes popular. The name stuck so hard in British everyday speech that it went generic, a bit like Hoover or Sellotape. These days loads of people say jiffy bag for pretty much any padded envelope, brand or not.
