Revelation 2: 12-17  The letter to Pergamum - speaks of  Jesus, "the One who has the sharp two-edged sword... "    In John's description of Jesus in chapter 1:16 he wrote.. "  and out of His mouth came a sharp two-edged sword; "  

My first observation when thinking about this sword, of course, is that it comes out of His mouth. We know from scripture that this depicts the Word of God.  Hebrews 4:12 "For the word of God is living and active and sharper than any two-edged sword, and piercing as far as the division of soul and spirit, of both joints and marrow, and able to judge the thoughts and intentions of the heart."  And Ephesians 6:17 ".. and the sword of the Spirit which is the word of God." 

The second thought is that the sword of the Lord is an instrument of judgement.
Isaiah prophesied in  49:2 " And He has made My mouth like a sharp sword.. "  Ezekiel also talks about the sword of the Lord. Ezekiel 21:3  " Thus says the Lord, 'Behold I am against you; and I shall draw My sword out of its sheath and cut off from you the righteous and the wicked.' " The Lord tells Ezekiel to " groan with breaking heart and bitter grief.. " The news that is coming will cause "every heart" to melt. All "hands will be feeble, every spirit will faint, and all knees will be weak as water."
The severe judgement of God is to be taken seriously.. more than seriously.. with groaning.. with grief.

This is the image that we must keep in our minds as we hear what Jesus says to the church.
It is true that they are living "where Satan's throne is.. where Satan dwells."  According to the Holman Bible Dictionary, Pergamum was the site of a temple dedicated to the Roman Emperor, Augustus.  It was also the site of an altar to Zeus. It was known for the worship of other idols also.
Jesus recognized that the church was holding fast to His name even in the persecution they faced. But, they were in danger of judgement because they were allowing false teachers to lead the believers away from the Truth.  "Repent therefore; or else I am coming to you quickly; and I will make war against them with the sword of My mouth. "  Jesus will fight for the Truth.  He will destroy the liar.  He has overcome and His Word will never pass away!

The blessings that Jesus promises to those who overcome.. those who stick with the Truth.. are "hidden manna" and  "a white stone" and a "new name".   We have this hope and promise in Christ as long as we remain faithful, abiding in Him and in His Word.

Father, keep us in Your Truth, in Christ, who is the Way and the Truth and the Life.  In Him, we abide, desiring to always keep Your commandments and to walk in the Light as You have told us.  Come, Holy Spirit and fill us once again. Amen.