Jealousy as defined by human standards is usually viewed as a sinful emotion. “Jealousy generally refers to the thoughts or feelings of insecurity, fear, and concern over a relative lack of possessions. Jealousy can consist of one or more emotions such as anger, resentment, inadequacy, helplessness or disgust” (Wikipedia). Notice that this description is based on a lack of something and wanting something that a person doesn’t have. Jealousy in the realms of romance is a lack of trust of the loved one or suspicion that the loved one loves another.
However, this is not what God’s jealousy is about. Since God is perfect, he doesn’t feel insecure or fear anything. He lacks nothing and he is omniscient so there is no suspicion in him. He loves us and he knows full well if we love another instead of him. And this is where his jealousy is always mentioned in the Bible. He is jealous for those he loves. He wants the best for us and it grieves him when we are rejecting what is best and care more for things that are actually worthless.
Since God is perfect in all things, love, holiness, justice, sovereignty, knowledge, wisdom, beauty, kindness, etc., what would be the very best thing for us? Would it not to know him and be in his presence forever, to love him? Would it not make sense then, that his perfect jealousy would want that for us and he would act on that jealousy to bring us to a knowledge of him through Jesus so we could spend eternity with him?