Pergola – I love my pergola at the back of our house. A pergola is an open structure, usually on regularly spaced posts or columns with a lattice or open frame top. This garden structure adds shade to a walk or passageway and is usually covered by climbing plants. I typically recommend lighter vines such as native vining honeysuckle or clematis instead of wisteria, which is much more strong and aggressive.
Arbor – Simply put, an arbor is a simple, less extensive pergola. Arbors are light, open structure formed from plants that twine together to form an arch overhead. They are also formed from a latticework frame covered with plants. Arbors can be metal or wooden and are usually in the shape of an arch.
Bower – Another form of an arbor is a bower. A bower is typically wider than an arbor and provides an intimate alcove where you can sit, relax, and contemplate.
Trellis – This is even simpler than an arbor. It is a structure of open latticework, especially one used as a support for vines and other creeping plants. A trellis is often freestanding and does not form an arch.
Veranda – This is a porch or balcony that extends along the outside of a building. Verandas are usually roofed and partly enclosed. We usually think of a veranda as part of elegant and expensive architecture.
Porch – We all know what a porch is. It is a covered platform at an entrance to a building that usually has a separate roof. Sitting on a swing under the covered porch brings back memories of cool summer evenings.
Portico - A porch or walkway with a roof supported by columns, often leading to the entrance of a building.
Gazebo –A gazebo is a small structure, usually roofed and open-sided. Gazebos are often located in gardens or parks where there is a nice view or focal point. Our gazebo is the focal point of our backyard gardens. It is screened in the summer and covered in the winter for more usability.
Solarium – A sun house or solarium is a building or room designed to receive maximum sunlight. Sometimes an enclosed porch is called a sunroom.
I'm sure you can think of other garden structure terms too. Regardless of the official name, garden structures add a great dimension to any garden.