Interaction can be difficult to define in a broad context as its meaning has many varying interpretations that are all dependent on specific scenarios. In its most basic definition, I think interaction can be defined as simply an experience. Taken further, an interaction produces an experience creating feedback that in some way alters behavior, but in order for this to manifest, there must be a two-way communication. The communication channel used can vary to great degrees, but ultimately the end result of an interaction will always be an experience.
The meaning of interaction from a modern designers perspective is slightly more involved as the communication channels must be made with the user in mind so as to create a clear and meaningful experience. As many modern designers rely on technology and the web as a communication medium, designing engaging interaction is one of the primary goals for any project. Without interaction, there is no meaningful experience, which will very quickly discourage any potential users.
Good design interaction occurs when the designer utilizes interface, logic and visual illustrations so as to fully engage the perspective user resulting in a dynamic experience. Many people would argue design interaction that is highly intuitive results in a good user experience; the less you have to think about something, the better the experience of using it becomes.
Utilizing intuition in design allows the user to interact with something faster. Since such emphasis is placed on the rate at which a product or application operates, good design can make up for slower connections and processors. These examples are only a minuscule component in the big picture of interaction.
Regardless of the specific circumstances through which an interaction is taking place, it should always be designed with the user in mind and should always be engaging. I believe that with these basic concepts in tact, a designer can create an interaction that becomes a unique experience that will draw attention and retain interest.