Long-Day Onions is a term used by people who grow onions. It refers to onions that need a large number of daylight hours to start plumping up below ground.Onions will form a bulb when the temperature and the number of daylight hours hit the right combination for them which triggers their clock. Long-Day onions will start bulbing when the day is 14 to 16 hours long (Short-Day onions need only 11 to 13 hours.)
These onions are better for people living in the north, where the summer days are very long. The long days give the onions the daylight they require to produce a good deal of top growth before they form bulbs (and the more top growth, the bigger the bulb.) When the day reaches the right number of hours for that variety of onion, the onion will stop forming top growth, and form a bulb instead.
Short-Day onions would start bulbing too soon in the north, before a good deal of top growth had happened, and so the bulbs would be small. In very northerly places, such as Canada or Scotland, which can have 14 to 20 hour days, Short-Day onions may never form a bulb.
Long-Day onions will never form a bulb in places such as at the equator, which gets only 11 to 13 hours of daylight — you will essentially just get a green onion.