Attention on the brain
Attention has a practical and specific online context. It has to do with managing the flood of data and advertisements vying for your time, which is finite. The metadata 'exhaust' (feeds, clicks, links, search terms, etc.) you create can become a useful tool to help filter and funnel information so that your time isn't wasted on irrelevant or marginal information you encounter online. It filters what enters your field of attention, based on implicit and explicit data. Attention is also about people and participation (tip to Mary Hodder)--who you influence, who influences you, who you choose to pay attention to or to avoid.
There is also the notion of 'intention economy,' which Doc Searls says is about people engaging online with a clear notion of what they want. "I want my intention to buy or find something to be serviced by the system, whatever it becomes. Hearing 50 companies tell me how they are competing for my attention doesn’t cut it; they are still looking at me as an eyeball," Doc said. It inverts the traditional advertising model.
Technorati CEO Dave Sifry extended that idea succinctly during the Search SIG discussion: "In the world of eyeballs, a good consumer is someone tied to chair consuming content and crapping cash. Participating in the growth of a site or community is about contributing to something larger than myself and receiving something from others."