Luke 1:1-4 - (the verses are above)
v1 - Other writings were apparently around. As an aside, this is how biblical historians note the dating and such of these texts. They don't just guess. Luke's came after Matthew and Mark probably, but before the siege of Jerusalem in 70 AD. Sometime in the sixties, 30 years or so after Jesus. Luke says "thing that have been fulfilled among us" which could also mean "things that have been surely believed among us" which is pretty important I think. He is really saying, look, let's leave the minor things alone and focus on the main thing; the things that have been surely belived. This is not like most of Paul's writings that deal with specific issues. He is writing about the important matters, namely Jesus.
v2 - This info was handed down by eyewitness. Christianity is no mythological, made-up faith. It has its roots in a person, and eyewitnesses of that person's life. Who is that person? Luke says, "the word" which isn't capitalized. But it's the same "word" as in John 1:1-2. This is Jesus. This stuff he is about to write about is from eyewitness and "servants" of Jesus. Awesome!
Only other things I'd like to note here, though other things jumped out at me, is verse 4. Luke is writing that we may be certain.
I write this blog that you may be certain that Jesus is the King. I write this that, even though you may not believe, you may wonder, may question, and may struggle with the realities of the historical and alive person of Jesus. Bring your questions, bring your concerns. See our lives, though invaded by sin, as we seek to honor the Holy One.