If something is the sneeziest, it makes you want to sneeze more than anything else.
The sneeziest thing might make you feel like you need to sneeze a lot, which can be annoying or funny.
Examples:
The flowers are the sneeziest things in the garden.
This room is the sneeziest room in the house.
The cat is the sneeziest animal in the pet store.
The sneeziest part of the movie was when the clown fell down.
The sneeziest pepper in the world made everyone sneeze at once.
The sneeziest pillow in the store made everyone sneeze when they walked by.