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the other one is '靠近方便, 贴近文明', both of which have different versions of English translations, most of them, though, suck. they go like:
One small step forward One giant leap toward civilization
A small step for man, A giant leap for mankind
Near the civilization Near the wall
close to civilization, Near to convenience
Are there any ones you guys find suitable and making sense to a western people?
The quote from your title:
'向前一小步，文明一大步。'
which literally translated to: "One small step forward, (is a) big step for civilization"
Is kind of a paraphrase of Neil Armstrong's "One small step for a man, one giant leap for mankind" which translates, according to Wikiquote, to:
'这是我个人的一小步，却是全人类的一大步。'
However, as mentioned above, this is a euphemistic way of asking people to get closer to the urinals in order to keep the floor dry and clean.
向前一小步， 文明一大步。
靠近方便, 贴近文明。
What they both want to say is: Please pee in the urinal, not on the floor.
They just say it in a very discreet Chinese way.
