What does Mark 3:14 mean?

The Bible doesn't say why Jesus chose twelve disciples, but it's probably to reflect the number of tribes of Israel. In Revelation, the New Jerusalem is described as having twelve gates, for the twelve tribes (Revelation 21:12), and twelve foundations, for the twelve apostles (Revelation 21:14).

The phrase "whom he also named apostles" is not found in some manuscripts in Mark 3, but it is found in Luke 6:13. Matthew 10:1 adds "heal every disease and every affliction" to their job description.

In modern language, it's common to refer to this particular dozen men as "The Disciples," but in reality Jesus had hundreds of disciples. "Disciples" is from the Greek root word mathetes and merely means a learner or someone who tries to emulate their teacher. An apostle is from the Greek root word apostolos and means a delegate or representative. Apostles are specifically commissioned by Jesus to preach the gospel. They will do so in Mark 6:7–13.

Although the apostles, to later include Paul and Matthias, are specially chosen by Jesus to preach, we are all called to spread the gospel (Matthew 28:19–20). Jesus' work on the cross is sufficient for salvation, but the news of what He has done must still be spread. Paul talks about this when he says, "… I am filling up what is lacking in Christ's afflictions for the sake of his body, that is, the church" (Colossians 1:24). Paul isn't saying his own suffering is necessary to save people, but that it appears to be necessary to get the news of Jesus to people.

To take on such significant leadership positions will require serious training, which Jesus will provide as the apostles travel with Him and learn from Him over the next few years. This method of discipleship is the blueprint for the Christian walk, as Paul tells Timothy in 2 Timothy 2:2. One lesson the twelve will learn is that to be a leader under Jesus' authority means to be a servant to all (Mark 9:35).