A track is a trace of somewhere that you have actually been (often called a "breadcrumb trail"). The GPS unit (external or internal) periodically sends details of the location which are recorded by the software, either by taking a reading based on a set time interval, based on a set distance, based on a change in direction by more than a certain angle, or a combination of these. Each point is stored together with its date and time. The resulting track can be displayed as a series of the recorded points or a line connecting them. Retracing your steps is a simple matter of following the track back to the source.
Route
A route is a preset series of points that make up a set route to follow for your destination. Most software allows the route and the track to be displayed at the same time.
Waypoint
Waypoints are used to mark particular locations, typically used as markers along the "way" to somewhere. They are either key entered by users or downloaded from other sources, depending upon the sophistication of the device. Although not linked to tracks or routes, they can be used to simplify the construction of routes, by being able to be re-used. Frequently, waypoints serve a "safety" purpose, enabling a route to be taken around obstacles such as shallow water (marine navigation) or streams/cliffs/other hazards which may prevent a safe passage directly from point "A" to point "B".
Platforms
Software can be used on a laptop computer with an attached GPS receiver. Most commercial software runs only on Windows and Mac OS X, yet some projects have started to support Linux as well. For most daily use however, a PDA, a dedicated device, or a smartphone might be handier. These devices can often also be used as a wireless modem for a computer, so that routing information can be uploaded or created tracks can be downloaded.