The Unusual Essence can be applied to any Greevil Egg (up to three times), which gives the egg in the icon a glowing ring for each essence applied. Although it won't be confirmed until after the event is over on November 12th, people are speculating that applying Unusual Essence(s) will give the courier that hatches from the egg unusual effects. Whether each essence applied simply gives it a greater chance of being Unusual or results in varying levels of visual effects remains to be seen.
Note that you can apply unusual essences to any eggs on top of the max nine essences you can infuse in the Greevil Egg (so you can create a Seraphic Egg using 3 Quas/Wex/Exort and still infuse Unusual Essences into it).