The following paragraphs give my understanding of the general concept of Irimi. I prefer to use Irimi for a Close With Partner.
Irimi means to enter or go through your partner. It is the yang or penetrating element in En On. Most Aikido movements begin with Irimi, even when one is doing Tenkan. In beginning practice Nage stands still until the attack is delivered, i.e. Nage stands until the arm is grabbed or Uke steps into Nage's space to strike. In more advanced practice Nage begins to control Uke before Uke begins the attack. This control is usually in the form of an Irimi to strike Uke. Irimi is extremely important because it instantly takes Uke off balance. The unbalancing is discussed in Off Balance.
Most Aikido techniques are done with Nage's body touching Uke's body. The initial Irimi closes the gap to get Nage close to Uke. Irimi must be a straight attack and yet it must come from the side. This concept is tricky to learn and even trickier to write about. The Irimi has to be perceived by Uke as a serious attack that requires defensive action. In other words if Uke does nothing the Irimi must take Uke down. It results in a throw such as Irimi Nage. On the other hand a highly likely defensive action is an attack on Nage. Discretion dictates that Nage avoid the attack by being on a line parallel to the line of the attack, removed from harms way. If Uke strikes straight at Nage, Nage moves to the shoulder of Uke's striking hand nearly brushing the striking arm or leg. A miss is as good as a mile but too large a side movement will draw the attack into Nage.