Affirmations are reinforcement of positive thought. The more you say them, the more you repeat them, you slowly begin to believe them. Then belief turns to knowledge, and when you know, your thinking starts to change. You begin to ignore the negative thoughts that plague almost all of us and doubt starts to lose its edge.
When I first began my journey, one of the things I repeated over and over, for a number of years, was "I am not a waste of space, I matter". It took a long time for me to believe that, and I now know I am not a waste of space, I do actually matter, and all the doubt, all the negative thoughts I had about myself, they all began to fade away.
The simple answer is, you're reprogramming your mind, building on your inner strength, blocking out the negative. And when that happens, Love and Positivity and Peace and Calm radiates from you and touches everything you touch.