"Christ is risen. He is risen indeed" - What is the actual meaning?

The phrase “Christos Anesti” is Greek for “Christ is Risen” and is an exclamation of joy and thanksgiving to God for the resurrection of Jesus Christ. This phrase has been used by Christians for centuries to physically and spiritually express their beliefs. (Citation) (my emphasis)

When a speaker says the words "Christos Anesti" (Χριστός Ανέστη, Christ is risen), the hearer's expected response is Alithos Anesti ("?ληθ?ς ?νέστη! ", Truly He is Risen! or "He Has Risen indeed!") (Citation)

LDS, but I assume this is actually cross-denominational, as it touches upon the very core of christianity.

Risen in this context simply means ressurrected. It is an affirmation of faith that Christ is ressurrected. For the individual, this can mean a variety of things, most notably including:

• since Christ is risen, we will rise too (see 1 Cor. 15). It should be obvious how a belief in a ressurrection can be comforting.
• since Christ died for our sins, and rose again, we can have faith that God can forgive us. This is of course very helpful for anyone experiencing guilt.
• Christ rose, so he was the Son of God as he claimed to be, so his teachings are divine. So for the individual this means it's a good idea to follow them.
• ...

But this is only the result of the faith that Christ really rose from the grave. The affirmation itself is just a simple exclamation of faith towards the ressurrection of Christ.

"Christ is risen. He is risen indeed" - What is the actual meaning?

This is in fact a ”Paschal Greeting” between two believers. One person offers the greeting     

"Christ is risen!"

and the response traditionally given is

"Indeed He is Risen!" or "He is risen indeed!"

Of course translations in English do exist.

From Wikipedia article Paschal greeting (with reformatting):

The Paschal greeting, also known as the Easter Acclamation or Easter Sunday Greeting, is an Easter custom among many Christian churches, including Eastern Orthodox, Oriental Orthodox, Roman Catholic, Anglican, Lutheran, Methodist, Presbyterian, and Congregational.

One offers the greeting "Christ is risen!" and the response is "Indeed He is Risen!" or "He is risen indeed!" with many variants in English and other languages (compare Matthew 27:64, Matthew 28:6–7, Mark 16:6, Luke 24:6, Luke 24:34).

Theories on origin

Credits for the origin of the greeting vary. However, the phrase "Christ is risen" is likely a shortened piece from Matthew 28:5-6, "The angel said to the women, “Do not be afraid, for I know that you are looking for Jesus, who was crucified. He is not here; he has risen, just as he said. Come and see the place where he lay."

There are two competing theories for the source of the response, "He is risen indeed." The first follows the tradition, not mentioned in the Bible, of Mary Magdalene bringing an egg to Emperor Tiberius. She then greeted the emperor with the words, “Christ is risen.”.[8] Others believe that the response comes from the Gospel of Luke 24:33-34 "There they found the Eleven and those with them, assembled together and saying, 'It is true! The Lord has risen and has appeared to Simon.'” [9] Regardless of the initial source, the phrase has become part of the Christian tradition. The greeting is used by many to celebrate the belief in the resurrection of Jesus Christ on Easter morning.

Examples

It is used among members of some Christian denominations when meeting one another during Eastertide; some even text or answer their phones with the phrase.

Eastern Orthodox

The greeting and reply are:

• Christ is Risen! – Truly He is Risen!

In the original language:

• Greek: Χριστός ἀνέστη! – Ἀληθῶς ἀνέστη!
• Greek-romanized: Khristós anésti! – Alethós anésti!

In some cultures, such as in Russia and Serbia, it is also customary to exchange a triple kiss of peace on the alternating cheeks after the greeting.

Catholic

In the Latin Church the traditional greeting on Easter morning and throughout the entire Easter week is:

• Latin: Christus surréxit! - Surréxit vere, allelúja
• English: Christ is risen" - He is risen indeed. Alleluia!

This ancient phrase echoes the greeting of the angel to Mary Magdalene to Mary, the mother of James, and to Joseph as they arrived at the sepulchre to anoint the body of Jesus: "He is not here; for he has risen, as he said" (Matthew 28:6).