What does evangelist and evangelism mean?
The word GOSPEL comes from the Greek word εὐαγγέλιον (translated as euangelion) or from the Latin evangelium as used in the canon of the four Gospels. Originally, the word εὐαγγέλιον meant "a reward given to the messenger bringing good news" (εὔ = "good", ἀγγέλλω = "bring good news"). The verb euangelion (translated as "evangelism") appears quite rarely in Greek literature outside of New Testament writings. Parallel texts in the Gospels of Mark and Luke use a synonym, the verb kerusso (κηρύσσω), which means "to proclaim." 
Some churches use the name evangelist for a worker who goes from place to place and from church to church, sharing the good news of the gospel. In this sense, the evangelist is different from the pastor, who deals with a specific local community. Many Christians of different denominations, with different theological perspectives, call themselves evangelists because they "spread" / share the gospel. Many churches believe that one of their major functions is to evangelize, to pass on their conviction that Jesus Christ is the Savior of mankind. 
William Barclay in his book A New Testament Workbook gives the following explanations for the gospel: In classical Greek, euangelion had two meanings: (a) “the reward given to a messenger for bringing good news, (b)“ the sacrifices made to the gods when they received such news, and in Greek (c) it meant "the good news itself."  In the Septuagint it is used to give the good news of victory (1 Samuel 31: 9), the good news of the birth of a child (Jeremiah 20: 9). 15) or simply good news of any kind.
The Evangelist, according to the Bible Dictionary is a noun (which appears only three times in the NT) derived from the verb euangelizomai, "to preach" and is usually rendered in translations by "preaching the gospel." It seems that in Romanian euangelion is usually translated as gospel, being a special word that appears more than seventy times in the NT, the word that sums up the whole Christian message: "the beginning of the gospel of Jesus Christ, the Son of God" (Mark 1: 1) and the whole plan of God's salvation through Jesus: “I declare unto you, brethren, the gospel which I preached unto you, which ye received, and wherein ye stand, whereby ye are saved, if ye keep it how I preached it to you; otherwise you have believed in vain. ”(1 Corinthians 15: 1-2)
Evangelism is the spread of the gospel through public preaching or personal witness, or to learn (trumpet, proclamation, preach) the gospel (the message from God that leads us to salvation / salvation) with the purpose / hope / desire to persuade / convert (according to : „Amplified Bible: Evangelism is teaching / heralding / proclaiming / preaching the gospel / the message from God that leads us to salvation, with the aim / hope / desire / goal to persuade / convince / convert). Another definition for evangelism is: "to communicate the gospel so that people can have the real opportunity to accept Jesus Christ as Lord and Savior and become responsible members of His Church" (after Dayton & Fraser). 
In the Lausanne Covenant it is written, “To evangelize is to spread the good news that Jesus Christ died for our sins and rose from the dead according to the Scriptures, and as Lord who reigns, he now offers the forgiveness of sins and the liberating gift of the Holy Spirit to all who repent and believe. Our presence as Christians in the world is necessary for evangelism, ... which is the proclamation of the historical and biblical Christ as Savior and Lord, in order to persuade people to come to Him personally and thus be reconciled to God. In presenting the invitation of the gospel, we do not have the freedom to hide the costs of discipleship. Jesus still calls all who want to follow Him to renounce themselves, to take up their cross and to identify with His new community. The results of evangelism include obedience to Christ, their integration into His Church, and responsible service in the world. ”
 Strong, The new Strong's expanded exhaustive concordance of the Bible, (Nashville TN, T.Nelson, 2001), 138.
 "Wikipedia: Evangelism",
 Barclay, Semantic Analysis of New Testament Terms, (Romanian Missionary Society, Wheaton IL, 1992), 163-64.
 Douglas und Hillyer, Bible Dictionary, (Oradea, Christian Book, 1995), 424.
 Underwood, B.E., 16 New Testament Principles for Evangelizing the World (Franklin Springs, Oradea: Advocate Press, SPMCR, 1988), 3–4.
 John R.W. Stott, The Lausanne Covenant: An Exposition and Commentary (Minneapolis, 1975), 20