Word "App" is short for Application. It is a term that has been used for many years in the Information Technology world. An application is a program or group of programs that perform a specific function.
The browser you use to see this and surf the web is an "App". This message board is an "App" on the Cruisemates server.
My favorite "App" is probably the browser on my Blackberry. I also love my Worldmate App that is basically a travel organizer. It keeps track of flights, hotel and cruise reservations. It makes it easy to bring up flight information, booking numbers, hotel confirms...etc.