The term "group" health insurance is generally associated with health insurance coverage obtained through a person's place of employment. Group insurance can also be associated with other organizations with a legally recognized structure and common interest, labor unions and professional associations (state bar & state medical associations for instance) are examples.
But, in the largest sense (by far), what most people are talking about when they refer to group health insurance is employment based coverage. Technically, in the group health insurance environment, the employer is the policyholder and the employer's covered employees and dependents receive certificates of coverage to identify their covered status under the employer's group health plan. As such, it is really a business/non-profit organization/governmental entity that obtains the health insurance policy for their employees so the employer is who can get the group health insurance and then any of their eligible employees can choose to enroll in it. In all but a few states for a business to qualify as a group it must have at least 2 eligible employees.
But, in the largest sense (by far), what most people are talking about when they refer to group health insurance is employment based coverage. Technically, in the group health insurance environment, the employer is the policyholder and the employer's covered employees and dependents receive certificates of coverage to identify their covered status under the employer's group health plan. As such, it is really a business/non-profit organization/governmental entity that obtains the health insurance policy for their employees so the employer is who can get the group health insurance and then any of their eligible employees can choose to enroll in it. In all but a few states for a business to qualify as a group it must have at least 2 eligible employees.