Wireless (or wi-fi) hotspots are essentially wireless access points providing network and/or Internet access to mobile devices like your laptop or smartphone, typically in public locations. To put it more simply, they're places where you can take your laptop or other mobile device and wirelessly connect to the Internet; some devices and smartphones also act as mobile wi-fi hotspots.
Typical wi-fi hotspot venues include cafes, libraries, airports, and hotels. Though many are free, some hotspots require a subscription or service with a particular mobile provider (e.g., Starbucks has exclusive deals with T-Mobile and AT&T customers).
Connecting to a hotspot and using its Internet connection basically works the same as other home or business wireless connection set up steps: Your wireless-equipped laptop or other device, such as an iPod or smartphone, will typically notify you when it is in range of available wireless networks. (If you don't get the "wireless networks are available" information prompt, you can go into your network settings to find available wireless networks.) You then just accept or initiate the connection to the hotspot's wireless network, which is usually identified in the network name (SSID). Some network cards will even automatically connect to the hotspot once it is in range, but this is generally a bad idea; for security's sake, follow our friend Bradley Mitchell's instructions for turning off automatic connections to unsecured access points.
One more connection note: if the wi-fi hotspot network is encrypted or hidden, you would need to get the security key and/or SSID information from the hotspot service provider to be able to locate and properly establish the network connection. Also, before allowing you to use their Internet connection, most hotspots will require you to accept their terms and conditions (which will generally require you to be a decent, law-abiding Internet citizen).