"Cloud" simply refers to things stored on a server somewhere other than your device. For instance, if you use Google Drive, you can store documents, music, etc. on Google's servers, and access it through your device. Same thing goes for all of the Google Play applications. TV shows, Movies, Books, Magazines, etc. are all stored at Google, and accessed using your device via wifi.
Some of these cloud services require you to do nothing but use them (like the Google Play stuff), while others require you to upload things to them so you can use them (like Google Drive, Dropbox, Box, etc).
Either way, cloud services are only available when you have an internet connection.