An extended day program is an after-school program held typically in an elementary school

Elementary school

An elementary school or primary school is an institution where children receive the first stage of compulsory education known as elementary or primary education. Elementary school is the preferred term in some countries, particularly those in North America, where the terms grade school and grammar...

 for students whose parents work beyond school hours. It is supervised by an adult or two and the kids play outdoors, sometimes on the playground

Playground

A playground or play area is a place with a specific design for children be able to play there. It may be indoors but is typically outdoors...

, or indoors, possibly in the gymnasium

Gym

The word γυμνάσιον was used in Ancient Greece, that mean a locality for both physical and intellectual education of young men...

or in a classroom. Often it is privately funded, that is, paid for by parents rather than by the school system.