Shodan is a search engine just like Google, with the difference that Shodan doesn't look for websites instead it looks for physical objects connected to the internet.
The most known thing connected to the internet is the router, an uncountable amount of households and offices, universities, schools or public spots like cafés and libraries have these devices to provide internet connectivity. A simple search on Shodan for 'router' results in 15.288.191 hits, that's 15 million routers whos IP-address everyone can find out, and everyone can connect to. Some of them don't have any kind of password security and one can directly connect with the router, changing whatever settings one can think of. Others have default usernames and passwords and the same thing here, anyone can login and for example change the default password so the person normally using the router is suddenly disconnected from the internet.
Dan Tentler, a well known IT security researcher, made some intensive research on Shodan trying to find as many open devices, and in fact he found a frightening amount of unsecured devices ranging from webcams, TVs, music stations and baby monitors to online crematoriums, school heating control systems, medical devices in hospitals and even power plants. With some expertise, really just a little, and a few clicks and you can remotely access all these devices connected to the internet.
Read more about it here: Forbes, Wired, NY Times, t3n (Deutsch), ...
Here is a very interesting talk about Shodan by Dan Tentler, a famous IT security expert:
Companies producing internet connected devices must be more cautious, they have to produce products which are much more safe and secure, this is the wrong end to lower the production costs. Security is becoming a huge factor in a internet connected world, producers and consumers need to be aware of that.