"Evangelical Christianity, or Evangelical Protestantism is a worldwide, transdenominational movement within Protestant Christianity maintaining that the essence of the gospel consists in the doctrine of salvation by grace through faith in Jesus Christ's atonement."
Well, that's the Wikipedia definition as far as it goes. But let me explain a bit further: The word 'evangelical' comes from the Greek εὐαγγελίου ('evangelion') or gospel or 'good news'. See Mark Ch.1:1.
In other words, we have some good news to tell to the world, ie 'The Lord Jesus Christ came into the world to save sinners.' (see what Paul wrote to Timothy in 1Timothy 1:15)
As 'Evangelicals', therefore, we believe that we have a duty to tell others of this good news in whatever way we can. We are not all called to be 'preachers' but whether we 'gossip the gospel', shout out on street corners, or just live a Godly life that others might observe, we want to communicate something of the transforming Love of Jesus.