Definition:
Interactive design can be defined the structure and behaviors of interactive products and service such as software and mobile phone (it can be other types of products and services) and user interactions with products and services.
Interactive products are designed to ground in an understanding of real users and attempt to improve the usability of product and interactive with people. I believe that good interactive design is to communicate a system's interactivity and functionality, defines behaviors that communicate a system's responses to user interactions and inform users about system state changes.
Examples:
Interactive design is concerned with the behavior of products, with how products work. It's not only about interaction with a product and interaction with a computer, but it's also abut making connections between people. Interactive design should be to create things that make people's lives better, which make us all more connected to each other.
These following links are good examples:
http://www.iminlikewithyou.com
http://www.iperg.org
http://www.tii.se/reform/projects/itextile/index.html
The image below is taken from http://www.funkdaweb.com/
FunkDaWeb are a leading and highly creative new media agency. Operating from Hale (Altrincham), FunkDaWeb Ltd has a passion for interaction, offering a wide range of services ranging from bespoke website design including Flash, ecommerce, content management systems (CMS), to logo design, graphic design and motion graphics.
The example below is an example of what interactive design is: