I know it's kind of hard to understand, so lets use a simple analogy. Imagine you have a big square parcel of land that measures 6 slogs long by 6 slogs wide. (a slog is a pretend unit of length about as long as a big suburban lot.)

Okay, imagine now that you're going to build eco-friendly housing for 36 families on your 6X6 slog parcel. Here are two ways to do this:

Master Plan A: Obviously, one way to do this is to subdivide the parcel into 36 1X1 slog lots and build a single family home on each one. Each house takes up 1/4 of the lot, leaving 3/4 of the lot as open space. The new inhabitants happily put in lawns, gardens and xeriscaping on their nice big yards. They don't like to walk 6 slogs to visit their friends across the subdivision, so they pave over some of their open space to make roads for their SUVS. Then they each need a garage and a driveway, so they give up some more open space for this. They also put in for each house street lighting, signs, natural gas line, electric service, water mains, sewer lines, and so forth. So they give up still more open space. They are left with less than 3/4 of the total 6X6 slog parcel as open space. And much more than 1/4 of the space is occupied by buildings and infrastructure. IOW, there are more than 9 lots of developed space and fewer than 27 lots of open space.

Now imagine a different way of subdividing the parcel:

Master Plan B: On one of the 36 lots, build a nine story condo building that covers the entirety of just one of the 1X1 slog lots. Each floor will contain four units for a total of 36 homes. Each unit, covering 1/4 of the lot, will have the same square footage as one of the private houses in Master Plan A. Since nobody lives far from their neighbors, they won't need SUVS. They will need public transit (elevators). This will be expensive, but not as costly as the roads, driveways and garages needed in Master Plan A. A lot more money will be saved because they don't have to extend utilities all over the parcel. Inhabitants will have 35 parcels of open space, on which they can plant gardens, lawns, xeriscaping, or just leave as wild land for the trees and birds.

Summary:
Low density Plan A yields 75 percent open space, minus much additional space needed for infrastructure.
High density Plan B yields 97.2 percent open space, with no space needed for infrastructure.

Magnify this times 1000 or times 100,000 and you can see the analogy to a high density or low density city.