Jasmine essence is, in the culinary sense, an artificial flavoring used in Thai cooking. The essence does not really alter the taste of the food but adds the fragrance of the jasmine flower. The flavoring is most typically used in desserts like jasmine rice pudding or jasmine coconut cake.
Look for this product in Thai grocery stores or purchase it online at ImportFood.com. Make sure to check the label to confirm the product is for food use.
If you don't have jasmine essence you can substitute one of these alternatives: