Dog agility is a sport in which a dog moves through an obstacle course with the guidance of his or her handler. Dogs run off leash, so the handler's only controls are voice and body language, requiring exceptional obedience training of the animal. In competition, both accuracy and speed are important.
Here are explanations of some of the more popular agility dog training equipment available:
Jumps are familiar to most people. A horizontal bar is supposed by a couple of posts. The dog jumps over the bar, which can be adjusted for height, ie. big dogs jump higher.
Other types of jumps are tire jumps (the dog jumps through a middle of a tire shape); panel jumps (several short panels instead of the horizontal bar; panels cover right from the ground all the way up to jumping height); and broad jumps (a set of slightly raised platforms that cover a broad area over which the dog jumps). All jumps are adjustable.
Tunnels are great fun for many dogs. Sometimes also called chutes, they're a hollow tube through which the dog runs. Tunnels are sometimes connected together to make a longer tunnel, or they can be "collapsed", meaning one end is open while the other lies flat. The dog enters the open end and pushes his way through the fabric until he exits the tunnel.
Weave poles are a series of upright poles through which the dog weaves. Many agility handlers say that this is a difficult task for dogs to learn, as it must be done in a specific way and dogs cannot "skip" poles. 
The teeter-totter or see-saw is similar to the see-saws children use on the playgrounds. Some dogs find it unnerving since they are required to run up one end, balance and wait for the other end to drop before they can get off. Dogs must touch the "contact zones" at each end of the teeter-totter to get full credit.
The contact zone are areas on the start and end of some pieces of equipment. Dogs must touch these contact zones with at least one paw when they ascend or descend the equipment.
The A-Frame is exactly what it sounds like: a platform hinged to form an "A" shape. The dog runs up one side and down the other, and is required to touch the contact zone on each side.
The dogwalk consists of a ramp leading up to a horizontal slat, then another ramp leading back down. The dog crosses the dogwalk, again touching the contact zone on each side.