This expertise represents the character's ability to tame, train, bond with, dominate, or otherwise manage animals and creatures for various purposes. Only a Force Sensitive character can use it to represent the Force abilities of Animal Bond or Dominate Beast, but any character can become a Creature Handler - the difference is simply in the methodology used. Be sure to roleplay accordingly depending on what makes sense for your character to be able to do.
Creature Handling refers to a character's knowledge of caring for, training, taming, feeding, raising, and otherwise handling non-sentient creatures according to conventional knowledge, skill, and practice. Anyone can learn this.
Animal Bond is a Light-Side or Universal variation which is more gentle, cooperative, and functions better with more peaceful creatures and is more difficult to use on particularly aggressive or hostile creatures but allows for forming a stronger bond that can last longer.
Dominate Beast is a Dark Side variation involving establishing dominance through fear, aggression, or a show of force. It allows for easier pacification and subjugation of aggressive predators, but if not maintained these creatures may turn on you or leave when presented an opportunity.
No Points: You can probably be trusted with household pets or animals that have otherwise already been tamed and trained, but you would have difficulty forming new bonds with creatures yourself unless they are very simple to care for. You are unlikely to succeed at giving commands to or persuading animals that aren't already familiar with and trusting of you, but through the Force you might be able to get creatures to provide you incidental assistance briefly.
1 Point: You can bond with creatures well enough that they give you some trust or deference. You can teach and give creatures simple commands such as 'follow,' 'stay,' 'attack,' or 'fetch,' make easy short-term requests through the Force, or cow a weaker predator from trying to hunt you. Through the Force, your Bonds or Domination are unlikely to last a long time without putting in effort to maintain them - you can enlist an unfamiliar creature for a short time, such as getting a creature to let you ride it for a short time, distract opponents, or intercept another animal seeking to attack you.
2 Points: Your familiarity with the animal mind is growing. You can better understand a creature's motivations and body language and attempt to interpret their emotions or state of mind a bit more reliably. You are more likely to be able to give slightly more complex tasks or instructions like 'guard,' and 'hunt.' Bonds and Domination through the Force is a little more resilient and deeper, lasting somewhat longer and needing less maintenance.
3 Points: You know animals quite well. You can care for them extremely capably and train them for complicated tasks, you know how to ward them away or entice them reliably, and a companion at your side may well be a companion for life. Through the Force, Bonds and Domination are strong now, and those you commune with this way will probably listen to almost anything you suggest or demand. Creatures of great power such as Krayt Dragons or Terentatek are still beyond your likely reach, but not impossible.
3☆ (Mastery): You are the animal whisperer. You have an almost (or literally) preternatural gift for communing with creatures both domestic and wild. You have a deep and intimate understanding of animals and can commune with them easily, almost as easily as speaking to another sentient. There are still limits to animals' non-sentient intelligence, and their ability to communicate back to you is accordingly rudimentary.