Linedefs are what make up the 'shape' (for lack of a better word) of your map. Every linedef is between two vertices and contains one or two sidedefs (which contain texture data). There are two major purposes of linedefs. The first is to give your map a definitive boundary between the player and the void (any area of a map behind a one-sided linedef is considered void space), and the second is to trigger action specials. Linedefs are also used to contruct sectors; a new sector is needed any time there is a change in floor or ceiling height or texture, light level, and so on.
There are three ways to trigger an action:
walkover
"use" (with the space bar, by default)
shoot
Which of these applies depends on the line type number.
The specified action will take place in the sector or sectors that have the same tag number as the linedef. Exceptions to this include local doors (which act on the sector on the other side of the line), special effects that apply to the linedef itself, and exit level.
Most actions can be specified as either once-only or repeating (by using different line types).