The ideal of the Roman culture at the time was to be able to say "I am content in all circumstances." So when Paul starts off with "I can do all things...", the Philippians would know he is referring to this ideal. The culture was focused on self-sufficiency to find this contentment however, Paul gives credit to the work of Jesus in his life for this change.
Humanity can accomplish great things but our calling is not just to get a job done but to be concerned with the spiritual aspect as well. Paul is not denying that he had to work hard, but that doesn't mean that he is equal to God in contributing towards the results. The praise belongs to Jesus.
Paul knew his limitations and understood without Christ's strength we can have ambition but will not be able to follow through. He also knew he could endure all circumstances, even death, as long as Christ is with him. This verse isn't talking about helping us avoid hard times, breaking free of difficult situations, or making our dreams come true; it is more that circumstances cease to be the determining factor in our contentment.
Being a Christian is about knowing the power of God in our lives. We often resist being put into situations where we are not in control, but this means we will not be able to truly rely on him.