why do plants grow better in a greenhouse

Controlling indoor air movement provides the greenhouse plants with a constant supply of carbon dioxide, which they need for sugar production. Although outdoor plants have sufficient carbon dioxide levels, strategically placed horizontal fans throughout a greenhouse allows air to press closer to the foliage for peak photosynthesis action.

The concentrated carbon dioxide results in larger leaves, stronger plant stems and possible early flowering and fruiting. However, air movement must be coupled with proper ventilation.

Closing off the greenhouse to outside air circulation lowers indoor carbon dioxide levels because the plants use the gas quickly while transferring oxygen to the air in exchange.
There are some tropical plants that die when exposed to frost; also, plants will grow more slowly when grown in lower temperatures than their native habitat.

A glasshouse/greenhouse allows in the sunlight (glass is transparent to visible light), but traps the re-radiated infra red heat (glass is reflective to infra-red): this is the greenhouse effect, which keeps the temperatures warmer.

By opening closing windows, it is possible to keep the temperature humidity in the optimum range for the plants inside.

For some types of plants, artificial lighting is used to help the plants grow - I imagine this could be useful when producing summer-flowering blossoms in the short days of winter. (The alternative is to fly them in from warmer climates. )