A Replacement is an non-participant who takes over the role of a player. Typically, players who are replaced have either requested it or have not posted for a very long amount of time (and thus are assumed to have flaked). In cases of moderator error, it is possible for the moderator to forcibly replace a player as well.
Replacements are generally seen as outside the spirit of the game. They are not directly responsible for the actions of their predecessors, and will be unable to answer for them. In addition, they bring an entirely different set of skills and level of play into the game that was not there previously. Last, they are not as affected by the Town's preconceived notions of the game state.
As a result, replacements have been known to enter the game as Town and completely destroy scumteams who otherwise had the game locked down. They have also been known to enter the game and effectively act like scum (as either alignment, but probably yours). The effect of a replacement is simply luck-of-the-draw.
With all that said, while replacements are against the spirit of the game, modkills are even more so. Thus, replacement is the better means for dealing with absent players.
Almost by definition, players will only need to be replaced when they cause a problem. The time it takes to search for a replacement is time during which that problem persists. Thus, it is not very efficient to start looking for a replacement the moment you need it.
The best way to deal with replacements is to get a few volunteers at the beginning of the game - people who want to be in the game but were too slow to sign up, for instance. Failing that, you should try to ask players you know are capable of coming in to replace. This way, you don't have to wait for players to come to you. Publicly advertising that you need a replacement is something of a last resort.