In terms of childcare where an educator is involved, it would make sense to appeal to the parents' concerns for the child's safety and well-being first. Next, the educator would want to prove that the daycare is a place where the child can be socialized and learn basic behaviors (such as playing well with others) as well as basic learning such as the alphabet and numbers.
For the child, I would think little is needed other than letting the youngster know there are other children to play with and plenty of toys. One difficulty may be dealing with separation anxiety on the part of child and perhaps even the parents.
Allowing the parents to tour the facility while other children are in classes would be wise to demonstrate the level of care being given, the instruction taking place and the daycare's overall sense of organization.
Sharing a file of recommendation letters might also be of help, as well as a listing of the state's licensing standards (and education/experience) of the employees, and the copies of licensing by the state. Other benefits of a childcare center include...
...increasing the quality of nutrition, raising immunization rates, and stimulating child development
Use of the word "educator" makes me assume that you are describing a daycare center. However, there are two kinds of daycare services available:
Child care can be divided into two types: center-based child care...and home child care...
In either case, the parents would need to know the benefit of leaving their child in your care as opposed to using a different kind of childcare.