Envy means you want what they have or their life style. There is some degree of idolizing or admiring a person that you envy. "You don't have to work this week? I envy you." or "I envy Hollywood stars that get to live pampered lives, not having to work normal 9-5 jobs." Jealous is more like someone did something that you wish you were there for, or that they weren't there to do whatever they did. I could say "Aww man, I'm so jealous you saw 周杰伦 last night, I wanted to go to that!" or, as the other guy said, for romantic feelings of jealousy, "Honey, are you jealous of that other girl? She's just my friend!"

The ideas are very similar, but I consider "jealous" to be stronger. "Jealousy" can also deal with rivalry in romantic feelings, which "envy" does not. I could easily say to someone, "I envy your going to London this summer." But it is much more difficult to say, "I am jealous."

"envy" means you want something someone else has: "I envy your skill at math." "jealous" means you want to protect something you have: "I don't even dare to talk her because her husband is too jealous."