Your Mentor is someone in your firm who is more experienced, can act as a sounding board and provide objective guidance and feedback. They can also help you increase your profile in the partnership. 

This person is normally the Head of your department or practice area. They are typically the person who will decide whether you are ready or not to go on Partner Track and be recommended for partnership. If you don't have their blessing to go for partnership, then it will be pretty much impossible to make partner at your firm. 

Your own coach helps you to take time out from the hurly-burly of your work life to focus on what really matters to you. They will also work with you in acquiring the key skills and knowledge required to make partner. An independent coach can often be the only person you can totally confide in without fear of risking your progression to partner.

Having a supportive and happy home life is important. It is very difficult to truly excel at work if you are having long-term problems with your family life. 

By going for partner in your firm, you are committing the next 5+ years of your life to this firm. Therefore, if you are going to be your best at work, you need to have colleagues whom you like, trust, respect and think of as friends.

Sadly, most of us, just when we are ready to accelerate to partner, also have conflicting priorities such as a young family. Regardless of your family situation, you do need a supportive 'other half.' If they don't support you with your career ambition, it's going to be hard work.