Q: "All of this sounds really great but I have never understood what it means to 'trust Jesus.'"
our A: First, trusting in Christ means that you're not relying upon yourself, but on Christ to get you into heaven. We cannot get to heaven by doing good deeds, things that we think will make us acceptable to God. Rather, we need to be forgiven of our sins, realizing that Jesus died for our sins. And what He did for us on the cross is the only way to have our sins forgiven. The Bible says...
After someone trusts in Christ for the forgiveness of their sins, a new life begins -- "If anyone is in Christ, he is a new creation; the old has gone, the new has come!" (2Cor. 5:17) The person becomes a follower of Christ. As a follower of Christ, a person relies upon Jesus in other areas of their life, not just for forgiveness of sin.
For example, Jesus said that He is the Teacher (John 13:13-14). He told His disciples that He would send the Holy Spirit to them, and that the Holy Spirit would teach them all things (John 14:26) and guide them into all truth (John 16:13). God teaches a person His ways and His truth. In terms of our values and our behavior, He cleans out stuff in our thinking that's not right, and shows us from His perspective what is correct. This is another way in which God loves us.
He is the One who knows all truth, and He wants us to build our lives on His truth. Jesus said...
The most important part of following Christ is to learn from Him. By relying on Christ as our Teacher, He guides us into living a new life that is according to His will and is according to truth. He shows us how to live, and will even guide us in how to pray. When we learn what He wants from us, then we rely on His strength and power (the Holy Spirit) to do those things.
Following Christ is all about relying upon Him. He told His disciples, "I am the vine; you are the branches. If a man remains in me and I in him, he will bear much fruit; apart from me you can do nothing." (John 15:5)