Unlike Twitter, Facebook, or Google+, LinkedIn is not primarily an online hangout or communications channel; it is more usefully understood as a cross between a dream phone book (one in which you could search people by any combination of company, job title, and keyword) and an atlas of human relationships (mapping who knows whom, worldwide), according to Alexandra Samuel in her short ebook Work Smarter with LinkedIn.
But why would you want a fancy phone book and an atlas of human relationships, and how could you go about getting the most benefit from it? To achieve business or personal goals, you often have to enlist the help of people you do not know personally, and you are far more likely to succeed in persuading someone if you can arrange for one of your contacts who knows the person to introduce and recommend you. LinkedIn is a key tool for gaining and maintaining these types of contacts.
Maximising the value of LinkedIn to yourself seems to require a fairly selfish and opportunistic approach. A large network of superficial contacts is fairly useless; the author advocates accepting only contacts who are likely to be useful to you in the future in a business sense, while ignoring and pruning connections with people who might be Facebook friends or Twitter followers but who are unlikely to be useful to your business.
The book includes a guide to getting a LinkedIn account set up in 30 minutes, as well as an interesting chapter on using LinkedIn in combination with TripIt to simplify and maximise the value of your business travel. The book will be of most interest to power networkers, but any professional with find it a good investment of the one hour or so that it takes to read.