One of the most unfortunate church-isms is the term "witnessing." It is usually used to refer to telling other people about Jesus or living a good life that makes people want to ask about our faith. You might, for example, hear a Christian say to another that they have been "witnessing" to their neighbors and inviting them to church.
The reason I say it's an unfortunate usage is not only because it's Christian jargon, and thus confusing to anyone who didn't grow up in church, but because no Christian living today is a witness. The original disciples of Christ who saw Him on earth and were there for His life, death, and resurrection were the witnesses. They actually saw those events. They witnessed them. We didn't.
We sometimes forget that not everything written in the Bible was said to us. We read the Bible looking for a special message to us, because that's what we were taught to do, when it's really an account of God's work throughout history, not necessarily a letter to us. It's for us, but it's not about us. So because of the misguided focus on ourselves, we often read a passage like Acts 1:7-8 and think it's talking about us when it's really Jesus speaking specifically to His disciples.
Acts 1:7-8 "He [Jesus] said to them, "It is not for you to know times or epochs which the Father has fixed by His own authority; but you will receive power when the Holy Spirit has come upon you; and you shall be My witnesses both in Jerusalem, and in all Judea and Samaria, and even to the remotest part of the earth."
Like witnesses at a crime scene, the apostles and earliest believers saw the events of Jesus' ministry on earth and were instructed to tell others what they had seen. They wrote down their testimony in the gospels and the other books of the New Testament and they told their stories far and wide. They then died horrific deaths for that testimony, without recanting it. They were the witnesses, and it was their testimony that made it possible for us to know what happened and to believe in Jesus.
When we tell someone about the gospel, we aren't "witnessing" to them. We're telling them what the actual witnesses said about the events they saw. We should also tell them about the evidence we have that indicates those witnesses were not making up their story, but were willing to die for it. Their deaths were not in vain, but are an important evidence of the truth of their claims. We didn't see what they saw. So, while our lives are certainly important, we aren't witnesses to the truth of Christianity because we didn't see the crucifixion or the resurrection.
We Christians today are believers. We are case-makers. We believe the witnesses who told us what happened and we believe in Christ who came to earth, died, and was resurrected to prove that He is God and can forgive our sins. We must make an evidential case to others for the reliability of the eyewitness accounts handed down to us. We also invite others to examine the testimony of those witnesses and believe as well.