This is a very good explanation . It is our testimony like you said to show the world that we want to follow in the footsteps of Christ.Let me tell you why I think baptism is important.
When one is baptized, it typically is at a church, surrounded by family and friends. It is a time when public declaration of your faith is made - a benchmark in your life, so to speak.
And during those times in life when you have doubts about your salvation and your relationship with God (which we all have from time to time) - during those times of doubt you can look back at your baptism and say for certainty "I know that I am saved, I made a confession of faith before God and man".
That, to me, is why baptism is important. And of course, it is also a testimony and example to others as well.
When I was baptism many years ago, as a baptismal gift couple in my church presented me with a James Avery ring. That was special, not only because it was a gift, but because this was a sincere sacrifice for this couple. He was a seminary student and she worked part time to pay for their small apartment.
That was some 38 years ago, and I still wear that ring today.