Aikido is often perceived to be purely a martial art and in its infancy, it wasn't much more than that. Initially, O Sensei, the founder, did not do too much more than develop the techniques that he learnt in his study of Daito Ryu Aikijujitsu. Even today, there are many who still train with this as their principal purpose. However, for the founder the art became more a way of life guided by a set of meaningful principles that were hard wired into the art. So much so, that he believed that aikido offered 'a way to reconcile the world', as fundamentally it became a practice of peace and love for him.
So this begs the question as to why he chose to practice peace and love through the medium of martial practice, which fundamentally is about learning ways to kill and maim. It was precisely because of this. that it proved to be the ideal medium. There is nothing more stressful than someone trying to physically harm us and if you can stay calm in this situation and bring about a positive resolution for both you and the attacker, then dealing with the rigours of daily life, should prove much easier.
Many of us spend a lot of time hiding our true selves from the world and depending on the situation, we wear different masks, but on the mat, we are faced with our true selves. If you are aggressive, fearful, timid, arrogant, uncertain etc. it will come out in your technique. You will see what gets in the way of you successfully practicing the techniques that you are being taught, and these will be the same things that get in the way of you fulfilling your potential off the mat too.
You have a choice at this point; to walk away and not acknowledge the problem, or to deal with it and transform yourself in to something better. That is why aikido is such an amazing practice and why it does literally have the potential 'to reconcile the world.'