Matthew chooses to end his account of the earthly life of Jesus with this 'great commission'.  The eleven remaining apostles were present - Judas the betrayer was dead (Matthew 27:3-10) - even though some of them were really not sure what was going on (Matthew 28:17).  Having clearly stated the basis of His authority (Matthew 28:18), Jesus gave them instructions for their lives' work, and the work for all of the world-wide Church until He returns.

The focus of this message was to go from where they were to make disciples by teaching the truth - as Jesus had taught them.  Jesus commanded His apostles to move from their homes (Mark 10:28-31) as they had previously practised (Luke 9:1-9), with the intention of explaining the gospel to people who previously did not know about Him.  That responsibility was not restricted to them, because Jesus sent out 72 others in the same way (Luke 10:1-24).  New disciples would be made from every people-group despite their different customs, religious habits and languages (Acts 2:1-12).  It was not an option for the apostles; it was a command to bring a wide diversity of people into His kingdom (Revelation 5:9-10).
 
Baptism was to be the external mark of these new disciples.  Their apprenticeship with Jesus needed an obvious beginning to their change of lifestyle.  Water baptism is the sign of a new start in a new life having repudiated the self-seeking path of sin, claiming forgiveness through the blood of Jesus (Acts 2:38).  Those people who know what it is to be overwhelmed by the love of God, and set free by His forgiveness, should affirm their new birth in baptism in the Name of God: Father, Son and Holy Spirit.
 
'Making disciples' of Jesus Christ is an intentional activity.  The Holy Spirit uses existing disciples to teach and challenge people to live in obedience to God's Word, to His glory.  It is not a task we can do alone, and it is not a task we can shun – it is a normal part of Christian obedience to tell other people how they can be saved.  That is how God has designed the Church to grow.  It will not always make you popular: sometimes it will lead to rejection, as Jesus was rejected too.  But some people will be saved, and they will praise God for you.  Don't be afraid: tell your friends and colleagues about Jesus, and then see what He will do.