Paul here gives a picture which the modern reader can completely understand. Just as there were athletes competing in the ancient games, there are whole careers today built on someone's ability to run faster or longer than others! We know what it takes to be the best, not just the ability, but the sacrifices and the mental toughness. Paul states unequivocally here that his intentions are to be the best and to complete the race and win the prize. Christians often seek to avoid anything that may be considered ambitious, but in the right place it is laudable. This is the race which is worth running with all the effort and commitment you can give it! It has the potential to be a very long race, with plenty of obstacles and pitfalls along the way, but the prize is the best ever offered: eternal life with God!
Paul is partly galvanised by the fear of disqualification. This might surprise us, as he of almost anyone had dedicated most of his life to serving Jesus. What might have made this fear more palpable? The man who termed himself, 'the chief of sinners' would have found himself challenged by the memories of what he did to the Christian believers. Those he now knew as friends, he had sought to persecute and destroy. God forgives us in His mercy and grace, but the memories of what we once were still linger, reminding us of what we would have become if it hadn't been for God's power at work in our lives.
Following Jesus is the supreme commitment of our lives, beyond raising children, successful careers, high income, good living. All else is shown for what it is when we turn our eyes on Jesus our Lord.