The oil in mayonnaise is what gives scrambled eggs that creamy consistency. The oil boosts the fat content in the eggs, and as a result, gives them a richer overall texture.
To try it yourself, whisk the mayonnaise directly into the eggs with your desired mix-ins before pouring it all into the pan. Use about one tablespoon of mayo per two eggs.
The resulting eggs will have a decadently creamy consistency. As for the flavor, you won't be able to taste any mayo in your eggs; it'll taste just like eggs, but better.