What is Apostolic Succession?

Apostolic Succession

Thank you ElderDad, I just finished reading it. It is a good illustration of the times, of the wave of heresy they had to face.
I liked Jerome the most, also Augustine and Irenaeus, then the rest.
Before posting this question I read all I could find in CCEL under this key.
Before that I took the word of the ecclesiastic institution (or how should I say? of the church as organizational institution) for it, and I do.
Now here is what I need to understand:

What happened was that the twelve closest disciples of Jesus Christ, whom we call apostles, were gifted by Christ (or rather received the Gift from God through Christ Jesus Who Is One with The Father) and are characterized in the Gospels as receivers of His Grace. (And also the other seventy close disciples are similarly empowered, characterized and charged with duties of which preaching (the doctrine) is one on the list of several, and was rather the explanation of deeds as to: how and why.
Whereas what I read about apostolic succession in the above mentioned bibliography is all about doctrine. What I had gained today from http://www.catholic.com/tracts/apostolic-succession is a better understanding of those times (the first few centuries AD) and an explanation for the focus on doctrine. Bur is it enough reason for this exclusive focus?

According to Matthew 10: 6-8
5 These twelve Jesus sent forth, … : 6… go rather to the lost sheep of the house of Israel. 7And as ye go, preach, saying, The kingdom of heaven is at hand. 8Heal the sick, cleanse the lepers, raise the dead, cast out devils: freely ye have received, freely give.

According to Mark 3: 14,15
14 [Christ Jesus] ordained twelve, that they should be with him, and that he might send them forth to preach, 15And to have power to heal sicknesses, and to cast out devils

Mark 6: 12,13
12And they went out, and preached that men should repent. 13And they cast out many devils, and anointed with oil many that were sick, and healed them.

According to Luke 9: 1,2
1Then he called his twelve disciples together, and gave them power and authority over all devils, and to cure diseases. 2And he sent them to preach the kingdom of God, and to heal the sick.

Luke 10: 1,9
1 … the Lord appointed other seventy also, and sent them … 9And heal the sick that are therein, and say unto them, The kingdom of God is come nigh unto you.

From the same early centuries AD as dates the mentioned bibliography, and into the second millennium, there are accounts about saints who, bishops or not, did the deeds, or rather, Christ worked through them, so that they spread the Word by Deed (or in contemporary verbiage: by their lifestyle): St Parthenios, St Benedict, St Columba, St Francis to name but a few.

My question is about this last paragraph here: What was this? Was it not Apostolic Succession?