When one sends this it is to convey a variant form of social greeting. It is directly derived from the word hey meaning hello or hi, but in this instance the extra "y" or "y's" are used to symbolize amount of affection. The more "y's" the more affectionate.
Girl: heyyy, I think you're pretty cute
Guy: Oh yeah, I think you're pretty cute too, are you down to Netflix and chill?