There are several important reasons to allow for prisoners to vote while incarcerated. The first and most overwhelming rationale is the democracy is predicated on the principle of "one person, one vote." Anything which violates this principle weakens democratic norms and places a country on a slippery slope of depriving citizens of the vote.
Next, there is the question of wrongful imprisonment. Not all people imprisoned for crimes are guilty. This means that someone who has suffered wrongful imprisonment is being doubly punished by being deprived of their voting rights. Even worse, there are people imprisoned pending trial who cannot afford bail but are innocent until proven guilty and should not be punished by being deprived of their voting rights.
Perhaps the most important political issue is that the prison population is disproportionately composed of the poor and of ethnic minorities, especially African Americans. For many offenses, African Americans are incarcerated at a far higher rate and for far longer than white people who have committed identical crimes. This means that rules forbidding prisoners from voting acts as a form of de facto racial and economic discrimination. The issue is further exacerbated by the fact that this is a demographic that tends to vote for Democratic rather than Republican candidates. Thus laws concerning voting by inmates have a strong impact on elections.