Approachability: The authentic magnetization of two people based on friendliness and common grounds 
A very simple and beautiful definition of approachability is given by Scott Ginsberg is; "The word approachability derives from the Latin verb appropriare, which means "to come nearer to." Interesting. It doesn't say anything about the approach-er or the approach-ee. Just "to come nearer to." Approachability is a two way street. It's both you stepping onto someone else's front porch; and you inviting someone to step onto your front porch."
A Supervisor in an ideal situation works toward maintaining good and healthy communication between him/her and the rest of the staff in every permutation or combination possible. By ensuring that employees exchange opinions and work related problems, a good supervisor is always in the driving seat to make excellent work group. By dealing with communication as a two way process, a culture based on free opinions and free from conflicts is established. supervisor has many different roles (e.g., organizer, leader, evaluator, director, planner, developer, and resource manager). Supervisor's position allows him/her to combine the talents of employees under supervision to accomplish the objectives of the company. This work group helps to meet two of the most significant challenges - to accomplish the task effectively and efficiently, and to provide fulfilling work experiences that develop employee capabilities and potential. Supervisor works toward identifying common goals of the employees and makes sure that they are occupied in completing those goals. A supervisor has to take entire work force together to achieve professional goals and also inspire the new employees to follow present work culture. He/she should hold an open hand attitude toward others while keeping a strict eye on the workings. Another key personality trait is approachability. This quality is related to your human dimension and to how comfortable that people feel around you. Remember, approachability can be crucial in many situations. Consider scenarios when employees have problems in their work lives or personal lives, when they make mistakes on the job, when they want to discuss their salary and when they want to express concerns about you. Employees also want to approach you with positive feedback and new ideas that can help the organization to improve. If you are not approachable, employees often feel too much distance and discomfort.
What is approachability
It is a trust between two people that each will be available for the other when needed. Always being open to discuss/help and interact with each other is the central theme of approachability. As one may say, it is a measure of whether the person in question is approachable How easy is the conversation flow with him/her
It is how your personality attracts and keeps people wanting to talk to you. In achieving this stage, most important attribute is your attitude and the way you carry yourself among a group. Every person is fond of interesting conversation, and also likes to increase ones knowledge base