A few months ago, my missionary companion and I were tracting (where we knock on doors and invite people to hear our message). We ran into a man who was somewhat familiar with the church and we started discussing the gospel. As the conversation progressed, he started talking about how there's no way I could "know" the church was true. I corrected him and told him that I did know it was true.
A testimony is the knowledge and witness that you've received from the Holy Ghost of the truthfulness of the gospel. It's like a rare posession--something that you hold dear and take good care of. Something that is literally yours and no one else's.
People spend much of their lives trying to acquire many valuable posessions in their life. Whether it's the latest iPod, most advanced smartphone, brand new car etc. While these things may bring temporary pleasure, they will all eventually break, rust and decay. A thief might steal it or natural disaster may bring it to its end.
But a testimony--that's yours to keep.