Holy jealousy means that one is appropriately possessive of something that belongs to him or her. For example, I am not willing to share my husband's heart or body with any other woman because he is mine. I'm happy to share his gifts and energies with the body of Christ and the larger world, and I even love to see that happen, but I want his heart and soul to be exclusively mine. That is a kind of holy and entirely appropriate jealousy.
Sinful jealousy is the desire to have something that doesn't belong to us; another word is envy. When we want something God has not given to us, such as other people's fame, or material goods, or a job, or favor, or a spouse, that is a sin. Sometimes we see this in a jealous person who wants all the attentions of their loved one to be directed to themselves. I have seen people who fly into a rage when they learn that their spouse or significant other has talked on the phone with anyone, or had any kind of conversation with a third person. Such a jealous person desires to have a level of exclusivity that doesn't belong to them.
God exhibits holy jealousy because our love and adoration rightfully belong to Him; He is jealous with a holy jealousy when we love and worship false gods in idolatry. His kind of jealousy is not sinful because we belong to Him and He created our hearts to belong to Him as well.