In the most abstract sense, interaction can be defined as the process that enables the exchange of information between two or more systems. When this process occurs, each system necessarily has an effect on the other. The information exchanged could be as simple as a binary state in computers to any other number of complex variables such that occur when human beings interact with one another. The key is that the systems have an exchange of information.
If no information is exchanged, no interaction has occurred. For example; staring at rock is not interacting with it because the rock cannot feel your gaze nor respond to it. However a moment of interaction occurs if you decide to touch said rock. Both entities are effected and you are in fact exchanging information. The process of physically contacting the rock creates an exchange of information that is minuscule but does exist. There is something there, namely the tactile sensation of it being harder than your finger. The rock in turn receives little information about your finger, but given enough time and poking each would conceivably erode the other, storing a physical ‘history’ of the interactions that occurred. Interaction necessarily effects the state of the systems involved. Its specific behavior is an emergent process that occurs to allow the exchange of information between two systems.