Let's approach it biblically and then we will come back to how it applies to you and I. We know that hope is necessary for a few different reasons. The first being that hope is needed when faith is involved. We know that "faith is the substance of things hoped for", so without hope faith is not produced. The reason many begin to lose their faith is simply because they have already lost their hope. This leads to the second reason hope is necessary, which is that without hope we are lost. Paul wrote to remind the church in Ephesus about this very thing by saying "That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world" (Ephesians 2:12). There is one final point about biblical hope that is the most important and I intentionally left out of the first two reasons. Our hope must be in Jesus Christ. Every other thing is fallible. If I hope in God and not the things of this world I can rest assured that I will be safe (Proverbs 29:25).
Hope is something that looks different from every person's perspective because we all have different situations, circumstances, and problems that our hope is being applied to. That is why it is hard to define on our own. What we can agree on, however, is that our hope is (or should be) in Jesus. He can be the "author and finisher of faith" or first and final say in our lives if we put our hope in him. It's then that faith has it's full potential and the things unseen can begin to become a reality. Put your hope in someone that will never leave you or forsake you and see how your environment changes. So how do we define hope? The answer is we don't, but God does.