The Internet Of Things (often: IOT) refers to the increase in devices other than computers or computer-like things being connected to the internet.
Most often these devices are appliances of some sort whose functionality is enhanced by being connected to the internet. Examples include everything from refrigerators with built in webcams so you can look inside from elsewhere, to home thermostats that allow you to remotely adjust the temperature, to lightbulbs that can be placed into existing sockets and yet still allow for remote control.
The term is a slight mis-statement, as there is no separate internet for things – it is the same internet used by all. The reference is simply to the growing collection of non-computer devices – devices we perhaps wouldn’t normally consider connecting to the internet – that are being attached to it to add an assortment of functionality.