In a normal Doom game, the game clock (see tic) runs at 35 frames per second. In a network game, this means that the players' inputs are sampled 35 times per second. These are placed in structures (called ticcmds), and transmitted to the other computers in the game.
If the ticdup option is used, the sampling occurs at a reduced rate. For example, if a ticdup of 2 is used, the sample rate is reduced to 17.5 times per second (half the rate). As a result, the amount of data transmitted per second is reduced by half. The computers in the game then "double up" the received ticcmd structures: i.e. the same ticcmd is used for consecutive tics.
The drawback to this system is the reduced movement accuracy. The reduced sampling rate means that the player has less precise control over their movement. The graphical framerate is also reduced.