Is this the correct definition of the greenhouse effect?

You have the right idea. It is like adding insulation to your house but it isn't as simple as that. Your house has a thermostat. If you add insulation, it will not warm your house, except marginally since the gradient of heat escape will be less but generally your house will remain at what your thermostat is set at. Similarly, there are thermostats in our climate that are poorly understood. The exact mechanism is not understood and why they change is not clearly understood. Part of it has to do with the melting and freezing temperature of water. Part of it is cloud formation. There are other factors as well. It is far more complex than a simple thermostat but it is also not as simple as some people suggest that adding CO2 is going to increase temperature a certain amount. They simply don't know all of the natural feedback mechanisms well enough to say how much of an effect it is going to have.