We have all failed. We have failed in our relationships. We have failed in our walk with God. We have all failed multiple times in multiple ways. That was true of Peter too. Peter had good intentions, just like we often do. But we learn from Peter that just because we fail, that doesn't mean that we will always be a failure.
We have all sinned, there is no doubt about that. A woman was brought to Jesus that had been caught in adultery. The crowds were ready to stone her to death, but after a few words from Jesus they all walked away. And rather than condemning the woman, Jesus offered her forgiveness and a change of life. He offers that to us as well.
There are times in our lives that the circumstances of life completely overwhelm us and leave us feeling hopeless. Like the woman who had the issue of blood, we have exhausted every resource, and tried every possibility, but nothing seems to work. Hopelessness comes from focusing on our problems instead of our Savior.