Believing in yourself can make your probability to succeed in something a lot higher. If you do not believe you can achieve something, you are keeping yourself from trying your best and this obviously can make things end up in failure. If others are involved in your goals, showing confidence in yourself will make them believe in you.
The first one who will and should believe in you is yourself. If you show others you are insecure and you cannot trust yourself, you cannot expect others to put their trust in you. Show others a strong image of yourself.
Once you become confident in yourself you will get inspired and will start to put more effort in working to achieve your goals. If you know you are capable of doing whatever you desire and put effort into it nothing can stop you.
Believing in yourself will make you have a positive attitude towards yourself and others. Working with a positive state of mind can make things a lot easier and enjoyable. It is hard to convince someone with a strong mindset that they cannot accomplish something. Try to have enough confidence in yourself to the point where no one or nothing can make you doubt your capacities.