A floating foundation is the foundation of a building that does not use footings. It is a poured cement slab that has two deep edges that go just below the frost line in northern climates. The foundation actually does float on the earth and moves as temperatures compact and expand the soil. It is very common in garage floors and mobile home slabs, and in many parts of the world, it's simply referred to as a slab foundation.
In a typical floating foundation, the plumbing and electrical lines are fastened to the slab by simply running them through the floor as it is poured. This means that the plumbing, drainage, and electrical lines must all be completed prior to pouring the foundation. In many cases, it is a much more affordable method of building than using a footing equipped foundation, but it can lead to very expensive repair bills if the plumbing requires work in the future. In warmer climates, the floating slab is much more friendly to homeowners as it does not flex too much because there are fewer extreme changes in temperature. It also helps to cool the structure, as the foundation's contact with the ground draws cool temperatures through the concrete and disperses them throughout the building.
When constructing out-buildings such as sheds, the term can take on another meaning. Some flooring systems for outside sheds are known as floating foundation floors and do not require any concrete to be poured. In these applications, the foundation is merely lumber framing placed upon blocks. This allows the floor of the shed to sit elevated off of the ground, which prevents water from seeping into the shed and protects the shed's contents.
When pouring a floating slab foundation, it is imperative to install reinforced steel rods or heavy wire mesh in the floor before pouring the concrete. The wire and steel prevent the floor from cracking and breaking as the slab flexes with the earth. Without this reinforcement, the slab will likely crack and possibly cause damage to the walls and ceiling, as the floor will be allowed to flex unevenly. Often, the flexing of an un-reinforced slab will cause doors to not close or open correctly and windows to stick or even crack. Walls are also subject to cracking, and drywall is prone to break at the seams.