Simply put, positive affirmations is the practice of using positive thinking in a consistent (daily) way to achieve your goal. It is a tool you can use to condition your mind to focus on one (or multiple) things you want to achieve.
Usually people who use affirmations do so to overcome negative thoughts or limiting beliefs that they were conditioned to believe at a young age.
In Eastern philosophy, many Buddhist monks chant mantra’s which is a form of “repetitive prayer”. Positive affirmations take their cue from this practice by using the “repetition” from chanting. So in a sense, positive affirmations can also be a form of prayer.
You can also view the Wikipedia definition here.