The economics of attention refers to the scarcity of attention. The basic idea is that people's attention is valuable because it is scarce. Sellers will pay to get peoples' attention.
Attention matters because business requires communication, and communication requires both a transmitter and a receiver of information. The internet has lowered the cost of transmitting information to practically zero; anyone can set up a web site or send out a spam email. But transmitting information is no use unless someone gives attention to it.
Unfortunately, people have a limited amount of attention. They can only give their attention to one thing at a time, so giving attention is costly for them. In the language of economics, there is an opportunity cost to giving something your attention — you need to "pay" for your attention to one thing by giving up your attention to something else. That's why they call it "paying attention."1
The economics of attention is the reason why the advertising industry exists. If you have someone's attention - such as by televising a beauty pageant or a football game - people will pay you to share that attention.
The term comes from economist Herbert Simon: "a wealth of information creates a poverty of attention."