General definition:
To make the surface of a horse’s teeth level and/or smooth, free from any sharp points on the outer edge on upper molars and inner edge on lower molars.

Why is floating necessary?
Because of the anatomy of the horse's teeth.  The upper cheek teeth (molars and premolars) are set wider apart than the lower cheek teeth.

There is very little overlap of the chewing surfaces, at rest, and there would be little contact of the chewing surfaces if the horse chewed up and down, like people do.  But horses have to chew side to side to get good occlusion or contact with upper and lower cheek teeth.  Horses can chew only on one side of the mouth at a time.

The anisognathic (unequal) position of the upper and lower rows, or arcades, of teeth, plus side to side chewing causes the chewing surface of the teeth to wear at a 15 degree angle.

The horse opens the mouth slightly, moves the jaw to one side. As the mouth closes the chewing surfaces shear off or mince the food. As the jaw returns to the resting position the chewing surfaces separate. When the front teeth, or incisors are in contact, there should be no contact between the upper and lower molar arcades.

What is the normal anatomy?   
  Adult horses may have up to 44 teeth.
  Six upper and lower incisors or front teeth.
  Four canine teeth, usually not present in mares.
  Two wolf teeth (some horses have 3 or even 4).
  Six upper and lower premolars
  Six upper and lower molars.
  The premolars and molars are collectively called cheek teeth or just molars.

Why should regular floating (once a year) be important to you as part of your horse’s care?
Because dental problems affect acceptance of the bit, behavior, performance and if for no other reason it affects your wallet.  One possible sign of your horse needing his teeth floated is dropping his grain out of his mouth all over the ground.  Hum, dollar bills in the bedding and manure.  Another sign is clumps of partially chewed grass or hay falling out of his mouth.

Simply removing the sharp points from cheek teeth may not eliminate all the sources of oral pain. Horses experiencing oral pain will not perform to their full ability.
Equine dentistry has evolved from just point removal to including a comprehensive oral examination, identification and correction of incisor and molar malocclusions. The shaping of certain cheek teeth to prevent soft tissue damage, therefore relieving oral pain. Complete records should be kept to document changes and improvement. 

What is malocclusion? 
Bad (mal) contact (occlusion). Horses can have incisor and/or cheek teeth malocclusions. Either type may interfere with grasping or chewing food and performance. Long standing malocclusions result in premature loss of teeth.

Incisors vs. molars?
Incisors are designed to bite off forage, after which the tongue moves forage back to the cheek teeth.
The cheek teeth crush and shear forage into small pieces, usually 1/4 to 3/8 inches long, so digestion will be complete.
The forage gets only one trip through the mouth and it has to be minced in this "food processor" adequately, otherwise absorption of nutrients is diminished.

Tooth Composition
Teeth have three main components; cementum, dentin and enamel. 
The outer layer is cementum. Cementum attaches  to the periodontal ligament, which anchors the tooth to the surrounding bone. 
Dentin makes up most of the tooth substance, gives strength to the tooth and surrounds the enamel. 
Enamel is the strongest substance in the body, but is brittle when compared to dentine. The combination of dentine and enamel give the tooth great strength, plus flexibility.  
These three substances wear at different rates, producing an irregular, rough surface capable of crushing very tough food material. 

Transverse Ridges
The chewing or occlusal surface of each cheek tooth, in addition to being rough, has a uniform "wavy" surface. Each tooth two "waves" or undulations. The undulations go from side to side of the tooth. This allows for better food grinding.
Exaggerated transverse ridges are ridges that are too tall and instead of having a rounded top, have a sharp point at the top. 
Exaggerated ridges interfere with normal chewing and jaw motion front to back. 

Wolf Teeth
Small, vestigial teeth usually found just in front of the upper second cheek teeth (second premolars). These teeth are the first premolars. Wolf teeth are not functional as grinding teeth. Wolf teeth are usually removed because they may cause pain when the horse is ridden with a bit. Sometimes wolf teeth are found in front of the lower second premolars. 

Canine Teeth
There are two reasons your horse does not have canine teeth.
1. Mares do not usually have canine teeth. If they do the teeth are very small and resemble wolf teeth. Canine teeth are usually one to 1.5 inches behind the corner incisor.
2. Your horse is less than 4 years old. These teeth erupt when the horse is 4 to 5 years old.