In order to understand the Greenhouse Effect one must first understand what a greenhouse is and how it works.
Greenhouses keep the temperature inside warmer than outside.
Sunlight (shortwave radiation) passes through the panes of glass.
Materials within the greenhouse (plants, floors, walls, benches, etc.) absorb this energy.
Absorbed radiation is reradiated as heat (longwave radiation).
The glass panes block the longwave radiation, thus trapping the heat, keeping the air warm inside the greenhouse.
The Greenhouse Effect can be defined as a system in which shortwave radiation is allowed to enter freely and is absorbed, then is reradiated as longwave radiation. The longwave radiation is then retained within the system.
Does the greenhouse effect in the greenhouse continue to work if the panes of glass are removed?

The gases within the Earth's atmosphere allow shortwave radiation to enter.
Some of the gases, liquids and particles absorb outgoing longwave radiation better than shortwave radiation.
Water Vapor (H2O)
Sources:
Carbon Dioxide (CO2)
Sources:
Methane (CH4)
Sources:
30 times more efficient at trapping longwave radiation than carbon dioxide
much less abundant than carbon dioxide
Chlorofluorocarbons (CFCs) - freon
Sources:
Ozone (O3)
- Sources - naturally produced in upper atmosphere, pollutants
Any solid or liquid particles within the atmosphere can absorb longwave radiation and reradiate it.
Sources:
Is the Greenhouse Effect a bad thing?
How can the Greenhouse Effect be harmful?