After speaking about the Rapture of the Church referred to in verses 13-17 Paul encouraged the believers to use the words he wrote as a means of comforting each other. There are several reasons why:
First, knowing that one day Christ will come and take believers home to heaven can be such a joy to those who are especially going through difficult trials and persecutions. This was certainly the case for most new believers in the 1st Century. It would be such a blessing for suffering Christians to know their trials would soon be over and they would enjoy eternity with their Lord and loved ones. That same comfort is for us to enjoy today.
Second, comfort doesn't just mean that "the end is coming." It can also mean that God will give us peace as we continue to serve Him here and now. Believers needed to know that trials and persecution did not come because God's upset with them! It does mean that God has a plan to work out in their lives and He may use suffering as a means for them to reach out to others who also suffer.
Third, "comforting one another" is also a testimony to the power and effectiveness of God's Word. "With these words" speaks of the believer using the actual Word of God in witness and testimony. Though our testimonies and explanations can be a joy to others, the real effective power comes from God's Word!