The first Kanji of Aikido, Ai, means to join. Aiki therefore is 'joining Ki', harmony or coordination. The power in Aikido comes from coordination but there are various levels to this. There is harmony within yourself, between yourself and others and ultimately with everything. On a practical level your technique will be transformed as soon as you stop trying to apply a technique "to" someone and realise that you are both part of one movement, one thing.
Harmony suggests separate paths coming together, forming a whole, and this is a very useful idea. But there is a further step, where harmony is understood as complete or one.
There is a rhythm to everything you do. This is not a matter of speed. It is a matter of timing. Move to and breath that rhythm. Do not try to force anything. O-sensei put it like this, "Heaven, earth and man must bind together as a single force. One must move in harmony with the cosmos propelled by the divine, Ki radiating from your body."
During practice we often use the term Aite to refer to whomever we are practicing with. Aite does not mean enemy or opponent but partner. This is how you should view any aggressor. From a purely Aiki perspective 'fighting an opponent' distances you from this most fundamental principle in Aikido, harmony. From a practical standpoint this also helps you avoid the classic pitfall of allowing anger to dictate your actions within a conflict.
There are various aspects to the lead. From offering openings and targets, and the Atemi, to drawing out the attacking force and redirecting it. When we lead the mind of an aggressor, their body follows, they are unbalanced and vulnerable. They struggle to regain their composure. We do not allow them to do so.
When you climb a staircase blindly in the dark and you tread on what you think is the last step and that step isn't actually there, you stumble forward. When you pick up an empty cup which you think is full, your arm shoots into the air. In Aikido, harmony often leads to these kinds of sensation in the aggressor. They are expecting some resistance, but there is none. They are expecting you to be there, but you are not.
So Aikido techniques are not a matter of 'throwing' with force. In fact, should you try to apply brute force you often give the Uke something solid to hold on to, which allows them to regain their balance. Consequently you lose the lead and are left in a purely physical struggle. Additionally, should you try to move too fast, to force the rhythm, the aggressor will break off and typically find themselves in a very strong attacking position.
In Aikido force is never opposed with force. We don't block and counter. We become one.
Atemis are strikes but they are often misunderstood as existing solely for the purpose of inflicting damage. Obviously should you find yourself in a situation where this is necessary you have that option. However their principle purpose is to lead the mind of the aggressor. An Atemi to the face for example can cause the aggressor to lean back, from there it is a simple matter to take their centre.
Despite appearances on the Dojo mat the Atemi is not to be confused with a feint. We might hope that the aggressor has the sense to get out of the way of an Atemi, but if they don't the Atemi will make contact.
Aikido is fundamentally noncompetitive. Competition separates you from your partner, the movement, from all that is going on around you. You want to win, to be better than some other, there is division, there is conflict, there is no harmony. Without harmony there is no Aikido. How you view a situation is vital. If you are competing you are involved in a struggle. If you are doing Aikido conflict ceases to exist.