Another definition that I like calls it an area of undeveloped land around a residential area created by covenant, deed restriction, or city zoning with the intention of preserving the open space and natural environment.
Here in San Antonio, for real estate purposes we have a lot description called "GREENBELT". I think that sometimes that description is rather loosely interpreted and what some folks consider greenbelt may not exactly fall into ANY of the categories listed above. What you can pretty much guarantee is that there is some undeveloped or unused land behind or adjacent to the home that is being offered for sale.
There are currently 36 properties listed as backing to greenbelt in the area where I live and specialize. Now this is a huge area and we do have some wonderful parks with walking and riding trails, some river authority owned property , some flood plains, some golf courses, and even some power lines. All of the above can fall into the greenbelt category, so it is a good idea to have a good look at the pictures of your real estate if you are looking online or even better idea to have your agent take a look for you. I just looked at the pictures of all 36 of these properties. I KNOW these houses and I KNOW these neighborhoods. Some greenbelts are absolutely fabulous! Some, not so much.
My house backs to property that I think belongs to the golf course. It may be owned by the River Authority because there is a part of the 500 year flood plain running through it, but it makes no difference to me. It is my own personal "BACK 40". It's a rough area of the golf course, far enough away from the fairways and greens to make it appealing, because we don't like golf balls hitting the back of the house. My next door neighbor has a path through to the course. Our greenbelt affords views of the wildlife, and we have a great place to walk the dogs. We can encroach with a sacrificial garden that feeds only the deer and rabbits. (The one thing they don't eat is parsley)