Yom Kippur is the day that Jews repent. It is a day that we are cleansed from our sins. Yet immediately after Yom Kippur is over we pray Maariv which starts with "Vehu Rachum Yechaper Avon". Then by Shemona Esrei we say Selach Lanu. Who had a chance to do a sin that we are saying this?
I heard this from the rabbi of my shul in the name of a Chassidic rebbe (I don't remember which one). The pasuk in Tehillim before vehu rachum (78:37) says
So the reason that we say vehu rachum is to ask Hashem for forgiveness if we said anything during Yom Kippur davening while asking for forgiveness which we did not really believe.
I also have my own idea about why we say vehu rachum after Yom Kippur. Sure we have just completed a day of intense prayer and fasting. We feel like we're on top of the world because we know that we have been forgiven. All through the day, we have committed ourselves to improving ourselves. Now that the day is over, though, we're going down to break our fast and indulge in our regular, every-day gashmius.
We return to regular life. We'd be fooling ourselves if we thought that we had reached the point where we will never sin again. We cannot remain on the level of Yom Kippur for ever. It is simply not possible for humans. We are imperfect, and as Yom Kippur ends, we acknowledge our imprefection by admitting that, although we will try as hard as we can not to, we will continue to sin. And so we ask God for forgiveness for the sins that will inevitably come.
1 - By the Slonimer Chasidim they actually do not say Vehu Rachum on Motzei Yom Kippur, they go directly to Barchu.
2- Sins that are between man and his friends are not forgiven unless we have asked for forgiveness from the one wronged even on Yom Kippur.
3 - I have heard in the name of Harav Shach Zatzal that when asked this question once Motzei Yom Kippur he responded ("Of Dem Vos Men Tracht Farvus Iz Du Aveiras Motzei Yom Kippur, Oif Dus Alain Darf Men Nuch Ah Kapara") Just for thinkink why there is sins after Yom Kippur, for this alone you need forgiveness.