When I was first asked the question, I had no access to the internet, so I thought, was it:
a circular building;
the big golfball from Epcot or
It made me picture many things. The Indoor Gardens at Kew in England (I’m always a gardener first), the movie Biodome (am I aging myself?), or the actual Biodome2 in Arizona? All I knew for sure was that I climbed on one as a jungle gym at my elementary school. What does it make you picture?
The Wikipedia definition is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The triangular elements of the dome are structurally rigid and distribute the structural stress throughout the structure, making geodesic domes able to withstand very heavy loads for their size.
Based on that definition they can encompass anything, it doesn't have to be a greenhouse, although that's the best use in my mind. The science behind how they are built just means that it’s one of the strongest and easiest-built buildings to stand up to wind/snow/rain. They have been around since just after WWI. They’ve built one in Antarctica and igloos have been used in the Arctic for hundreds of years. Dome structure equals strong.
One great quote I found from a company you can purchase a geodesic dome kit from said: Domes are a true example of “doing more with less.” A dome encloses the largest volume of interior space with the least amount of surface area, thus saving on materials and cost. Since a dome is free-standing, air and energy circulate without obstruction, enabling natural heating and cooling.
But of course, you could always get the plans and make one yourself from recycled materials. That would be a great project in the “REUSE” part of the 3R’s.
Considering they are so strong, that makes one wonder, will they eventually be built on Mars?