What Does "Bear Witness" Mean In The Bible?

What does the word "witness" mean in the Bible? Isn't a witness just someone testifying in a courtroom? Why does Jesus keep saying He "bears witness"? And how can we bear witness today?

In the Gospel of John, we see an interesting dialogue between Jesus and Pontius Pilate.

So Pilate entered his headquarters again and called Jesus and said to him, “Are you the King of the Jews?” 
Jesus answered, “Do you say this of your own accord, or did others say it to you about me?” 
Pilate answered, “Am I a Jew? Your own nation and the chief priests have delivered you over to me. What have you done?” 
Jesus answered, “My kingdom is not of this world. If my kingdom were of this world, my servants would have been fighting, that I might not be delivered over to the Jews. But my kingdom is not from the world.” 
Then Pilate said to him, “So you are a king?”
Jesus answered, “You say that I am a king. For this purpose I was born and for this purpose I have come into the world—to bear witness to the truth. Everyone who is of the truth listens to my voice.”
— John 16:33-37

Jesus has come into the world to bear witness to the truth.
This is his purpose, the very reason He has come into the world. He was born so that he would bear witness to the truth. Chances are, if you are reading this you have decided to follow in Jesus’ footsteps, to be a disciple. A follower. We follow a man who told us in this exchange that his purpose was to bear witness to the truth. We need to go do the same. 

How can we bear witness today?

When you're with friends in class do they see what Pilate saw? At work, are you a witness to truth or something else?

It is so easy to forget that this is all true—that Jesus is who He says He is.

All the hope of the world is wrapped up in this truth. This is why our company even exists. We create stuff for one purpose: to bear witness to the truth that Jesus is the truth. That Jesus is the very essence of life. Of living. Of breathing. The hope being that a shirt or sticker, like even this Bear Witness design would make someone ask.