Seasonal Pennants are granted to players who participated in Seasons in Diablo III, beating Chapter 4 of Seasonal Journey. Not every Season offers a Pennant reward: so far only three, Seasons 3, 6 and 10, have such rewards, while other Seasons had pets instead.
When obtained, Seasonal Pennants can be added to Wardrobe. Only one pennant can be used at a time. If equipped, it will be visible even in character selection screen.
Season 3
Season 3 Pennant does not have a special name. It is fashioned in form of Diablo's head on a pole, with the game's three vertical stripes on a black banner.
It also comes with a portrait frame of similar design.
Third time is the charm.
You braved the depths of Season 3, and this is what you found.
Season 6
Season 6 Pennant is named Samhain. It is fashioned in form of a Reaper scythe, with a Reaper's hood on top, spine as shaft and a silver demon's head on a pale blue banner.
On the last day of harvest season, the wisest folk lock their doors, hang their wards, hide under their beds, and wait for dawn.
Season 10
Season 10 Pennant is inspired by the Book of Cain, with the shaft in form of a cathedral chandelier, and the banner itself being a large Horadrim scroll with a sigil on it.