Refers to a lengthy Hadith where Prophet Muhammad(saw) was observing I'tikaf in the Masjid when his wife, Hazrat Safiyah(ra) came to visit. When she was leaving, he escorted her out. On the way, two men were walking in. He had them wait while she left so she would not be seen unveiled. Afterwards he told them who she was and said: "I have identified her to you lest the devil make mischief and put a wrong idea in your hearts."
Now who on Earth, especially from the Sahaba, would suspect the Prophet(saw) of anything wrong... not only that but in Ramadan, the last 10 days, in I'tikaf, and in the Masjid Nabi! This was done to set an example that one should do everything possible to prevent themselves from being slandered.
There are two principles here. The one everyone knows is that it prevents a potential slanderer from slandering and thus saves them from sin. 'So what' you might say, it was the Prophet(saw)'s job to worry about other people, not ours. Blatantly incorrect. It is your duty to avoid letting other Muslims sin. Plus the other principle at play here is that you have rights over yourself. You have a right to not let yourself be thought of negatively or let people imagine wrong things about you. Protect yourself from others' intentions, if you do not take care, how can you expect Allah to act on your behalf out of His care if the situation repeats itself, albeit at more cost to you the next time?
Some of the longest Hadith are of this topic because it requires a narration of the entire situation to understand. It is important.
How does one suppose that those entire Islamic societies were built? How do you find that kind of a quantity of good people? By helping each other become that way. Saving someone from sinning by robbing them of that opportunity might keep their souls on the right path just enough to avoid another major sin and so on and so forth.
This is important because Western society has the exact opposite principle. Rather, it fosters off this kind of suspicion amongst its citizens because it markets so many things to that suspicion and profits. A basic example: A man comes home and his wife smells perfume on him and demands to know where he's been. "You don't trust me?!" he indignantly responds. Bullshit. That's the way things work here, people demand others to be in love with them to such a degree that they abandon logic and their minds. That's one party loving their Self entirely too much, they want to be loved but not love or engage in mutual love. This also illustrates how trust comes not just from love but is also built logically on piety or taqwa. Living a life of good character and morals actually translates into seemingly non-related things like loving or being able to be loved (and thus the issue of trust) having formed a more solid foundation.
And that's between the closest relations. There's no concept of avoiding slander otherwise and when Islamic and Western identities collide, like in the South Asian community in North America and Europe, people will struggle adapting the Western mode of thought to a foreign sub-culture or environment.