Jealousy is a normal emotion with which a person can have a healthy relationship. Feeling jealousy is usually a sign of something bigger going on, primarily one's current situation and place in it. It's extremely important to communicate about jealousy in any relationship, and gets even more important in polyamorous relationships.
Most often, jealousy is a prominent aspect of the fear of abandonment. So long as jealousy is kept in check and doesn't explode, this fear can be alleviated through reassurance from one's partner. Dismissal, invalidation, and neglect all exacerbate jealousy as they reinforce the fear of abandonment.
Sometimes feeling jealousy is brought about due to the partner's behavior. Communicating jealousy should include learning how each person wants to be reassured - this would best be done as part of the polyamory discussion (negotiating time and safety and boundaries, etc.) but may change as time goes on. For some people, simply having sex more often is enough reassurance; for others, it works to have a date together for each date a partner has with other people. And if you can't specifically name what would be reassuring for yourself, it's ok! Experiment! Eliminate what wouldn't work! It's a process, like all aspects of relationships. When one's partner isn't willing to work together or insists on using only their own reassurance method, there are more issues in addition to the fear of abandonment.
And sometimes feeling jealousy is brought about due to an individual's emotional state. Many people feel the fear of abandonment at different times in our lives for many different reasons, regardless of the current relationship(s). An unhealthy relationship can certainly worsen that fear and sometimes a very healthy, involved relationship can alleviate an individual's fear - I recommend against using relationships for that, though. Overcoming one's own fear, especially when it's been validated in the past, is very difficult and scars can so easily be re-opened. Small steps, self-care, distance from incompatible/disrespectful people, and intrapersonal communication help one overcome that fear and heal from whatever has brought it about.
And sometimes jealousy has nothing to do with fear, it's envy of another person's situation and that's it. When one's partner is out of town and having fun for example, it's entirely possible to feel jealous without fear or resentment - this is neither unhealthy nor healthy, it just is. It's possible to feel both happy for one's partner (and the people they see), jealous of them, and have fun on your own all at at the same time. Usually treating oneself to something special can eliminate this envy, or at least push it to the background until the situation changes.
Above all, learning to listen to one's emotions, figuring out where they come from and what they're telling you, and handling them them in a healthy way (working out at the gym, partying, cuddling with kitties, crying over a pint of ice cream, whatever) are vital to functioning as both and individual and a partner. We all mess up sometimes, learn and apologize and move on.