“But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth.”  Acts 1:8

Every Christian should be a witness- this is not a negotiation or a suggestion, it is Jesus’ dream and instruction and if you love and serve him you would live your life with this truth as priority.
A witness is different from a preacher, a preacher announces- brings information (in this case, the gospel) to his/her listeners, he tells them what he heard/knows; a witness goes further and provides evidence that what is being said is true and even more detailed, a witness confirms his presence during the event.
Jesus is alive in you! He’s not dead; he doesn’t expect you to just talk about it, he wants you to prove it- and so when he gave his fervent instruction:
“And he said unto them, Go ye into all the world, and preach the gospel to every creature.”  Mark 16:15
He mentioned that they would prove their message; they would do the things he did while he was on the earth because he is alive in them.
“And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues; They shall take up serpents; and if they drink any deadly thing, it shall not hurt them; they shall lay hands on the sick, and they shall recover.” Mark 16:17-18
This is why he said the Holy Ghost is needed; he give you the ability to witness, just like he did the apostles:
“And with great power gave the apostles witness of the resurrection of the Lord Jesus: and great grace was upon them all.”  Acts 4:33