They’re called something like Breathe Strips. They have two rigid-ish inserts along the length and are very sticky. Sticking them across the nose is supposed to slightly pull open the nostrils, thus aiding breathing.
I’ve seen rugby players with them as with a gumshield and jaw clamped to avoid fracture in contact, a lot of breathing is via the nostrils.
However, in cycling, most of the breathing is through the mouth, so I don’t think it would really help much.