ANSWER: First, let us take a look at the scriptures in question. In Matthew 25, Jesus states he will gather up all people when he returns to the earth as King (verse 31). He will then divide them into two groups - the sheep and the goats.
He will place the sheep on his right and the goats on his left (Matthew 25:32). He will then say to the people on his right, "Come, you that are blessed by my Father! (those who lived a truly converted life and obeyed God) Come and possess the kingdom which has been prepared for you ever since the creation of the world." (verse 34).
Christ will then turn away from the sheep and state to the "goats" or those who are on his left, "Away from me, you that are under God's curse! Away to the eternal fire which has been prepared for the Devil and his angels!" (Matthew 25:41).
This parable is about the time of the judgment. The sheep are symbolic of those who follow and obey Christ, while the goats represent those who chose not to follow Jesus and His example on earth (a witness).
One overlooked fact concerning this judging is that Jesus considers one set of animals HIS ("as a shepherd divides HIS sheep . . . ", as verse 32 is translated in the NKJV) but the others he does not! He owns (we have be bought and redeemed by him at a price - 1Corinthians 6:20, 7:23) and is the true shepherd over the sheep or those willing to follow him and do what he says. He does not, however, claim ownership or responsibility over the goats! They are those who are rebellious and stubbornly refuse to follow anyone anywhere. Their ultimate fate is to be thrown into the lake of fire.
The real point of the message, as you have likely guessed, is the difference in behavior between the two groups - the sheep and the goats. One group is merciful, kind, generous, loving and willing to do whatever it takes - even at their own expense - to help out another fellow human ('the least') in true need. Jesus regarded their actions as personally affecting him.
Because of their unselfishness and giving behavior the "sheep" inherit God's kingdom. The other group, the "goats," is selfish, self-centered, self-absorbed and self-seeking. They are rejected in the judgment.
Jesus' sheep and goats parable can thus be summed up: LOVE is the answer. Those dedicated to loving will receive love in return from all others of a like mind. But, where there is no love given, none will be returned. No love, no Kingdom.