I grow these around the Crepe Myrtle in the front yard. In the summer, Crepe Myrtles in this area are attacked by small, almost unseeable insects which leave the foliage covered by a sticky sap... which then becomes covered with dust and debris which stick to it. There are several insecticides that you pretty much have to spray every two weeks, but I heard that planting an onion under the bush will 'flavor' the shrubs sap and keep the bugs off. Since the bush was in the front yard, I decided that the Egyptian onions were odd enough to be interesting... they've been there two years, and no sticky, icky leaves... As to them flavoring the crepe myrtles sap... I have no idea, as I have never tasted a crepe myrtle leaf to find out, and I have no intention to do so in the future.
The onions grow long stalks that sprout miniature onion bulbs, which then can sprout even smaller onion bulbs on the end of their leaves, as is happening in the top pic... Now the parent plant tends to be too tough to eat as scallions, but if you pull the bulbils apart and plant them, in a few weeks, they'll be nice tender scallions for cooking or salads. Also, the small bulbs are sometimes taken off, allowed to dry and the leaves die back, then pickled. I've never done that, as I like scallions too much.
Left on the plant, the stems will bend over, and the bulbils will sprout where they touch the ground... about 2 or 3 feet away. Hence the name walking onions, as they seem to be walking across the yard...
The real reason I got these though, is that I remember almost every house in the neighborhood had these when I was a kid... Strange how some things stick with you. I also have a fondness for sunflowers and hollyhocks by wooden fences, for the same reason. (but only the single hollyhocks, the double pom-pom ones just don't look right to me.)