Ceremonies and ritual
Nature can provide a backyard wherever it is conducive for the purpose and activity. Here Medicine woman Sakina Blue Star is conducting a ceremony in a sacred circle gathering. Wherever you have earth and sky, you can perform a ceremony.
Formally designed spaces in a garden make ceremonies a special purpose type of use and depending on the kind of ceremonies performed, the space needs to be designed around its function such as how many people would normally attend. Outdoor areas are usually selected due to the higher number of people or to allow for unexpected guests to show up.
Altars can be set up outdoors or indoors depending on how public or private the purpose.
Altars are most commonly associated with some form of religeous practice or honoring a diety or belief system. Even Nature as an entity such as Gaia is celebrated by neopagan groups often during auspicious times of the year including the soltices and equinoxes.
Stonehenge, shown below, can be recreated in a smaller setting in one's garden using monolith type stones around which ceremonies and rituals can be performed.