It became a symbol of revolutionary justice. Earlier on, that spot was held by the street lamps, after the lynchings in 1789 where people were hanged from the lamp posts. Its use as a symbol is mostly associated with the Reign of Terror, but there are songs and poems celebrating the executions of "Terrorists" in the years after.

The audience at public executions was seen as legitimizing the execution. The people gave their support and permission by watching. It made the onlookers participants in the victory of the revolution against its enemies, even if they were otherwise disqualified from taking up arms. That's why it was primarily women who watched executions, since men with the same need to aid the revolution could do so more directly. source: The women of Paris and their French revolution, by Dominique Godineau.

It was given a lot of nicknames, like the National Razor, or the Patriotic Shortener. The name "guillotine" itself is a nickname, though a less affectionate one. It was originally named that to make fun of a politician, Guillotin, who argued passionately for its use. Contrary to popular belief, he didn't invent it.

A large number of people (I've seen estimates from 13 000 to 16 000) were executed with the guillotine, but the idea that the practicality of the machine itself was a reason for the high body count is false. In reality, the guillotine was slow, expensive, and cumbersome. Drowning or shooting was much easier and used when large numbers were to be killed at the same time. As far as I know, the largest number of guillotinings in the same day was 70 or so, which is nowhere near the number killed in mass drownings, where some estimate that up to 400 were killed at the same time. The number of guillotinings in Paris during the Terror went from an average of 2 a day during the autumn of 1793 to 35 in June-July of 1794.