what does "the Apostolic Blessing" mean ?
The Apostolic Blessing followed:

"Ego facilitate mihi ab Apostolica Sede tributa, indulgentiam plenariam et remissionem omnium peccatorum tibi concedo, et benedico te. In nomine Patris, et Filii, et Spiritus Sancti. Amen."

"I, by the faculty given to me by the Apostolic See, grant to you a plenary indulgence and remission of all sins, and I bless you. In the name of the Father, and of the Son, and of the Holy Ghost. Amen."

Question

what does "the Apostolic Blessing" mean ?
The Apostolic Blessing followed:

"Ego facilitate mihi ab Apostolica Sede tributa, indulgentiam plenariam et remissionem omnium peccatorum tibi concedo, et benedico te. In nomine Patris, et Filii, et Spiritus Sancti. Amen."

"I, by the faculty given to me by the Apostolic See, grant to you a plenary indulgence and remission of all sins, and I bless you. In the name of the Father, and of the Son, and of the Holy Ghost. Amen."

Answer

Apostolic Blessing is a special blessing, proper to the liturgy of the Catholic Church.

Answer

It's a blessing which confers forgiveness of sins.
http://www.sanctamissa.org/en/resources/books-1962/rituale-romanum/36-the-sacrament-of-the-anointing-of-sick-apostolic-blessing-plenary-indulgence-at-the-hour-of-death.html