Did he really sacrifice him
I'm confused why you are asking, as the text seems quite clear that Isaac was not killed. The language of verses 10 and 11 ("Then he reached out his hand and took the knife to slay his son. But ...") already clearly suggests an interruption before Abraham could complete the sacrifice. This is even more clear in verse 12 ("'Do not lay a hand on the boy'", which would make no sense if Isaac were already killed) and verse 13 ("[Abraham] sacrificed [the ram] as a burnt offering instead of his son").
So, no, Abraham did not complete the sacrifice; Isaac did not die.
If you are confused by the later verse 16 ("'... because you have done this and have not withheld your son ...'"), this is not referring to an accomplished act, but rather to Abraham demonstrating that he would have followed through had he not been stopped.
Why did God command Abraham to sacrifice Isaac?
In addition to a testing of Abraham's faith (see Ray's answer), many Christians see another reason, which is foreshadowed in God's words: "Take your son, your only son, whom you love". Parents are frequently willing to give their lives for their children, and as such, sacrificing one's son, especially an only son, is perhaps the greatest sacrifice conceivable.
Jesus Christ is the only son of God, whom God loved (Matthew 3:17).
In Abraham's case, God intervened at the last possible moment and provided a substitute. But for the sake of us sinners, God himself made the ultimate sacrifice of His very own Son. Thus, many consider the testing of Abraham to be a foreshadowing of Christ's sacrifice.