the ways it's used basically end up being one of these two things
software as a service:
instead of buying a licence to microsoft word and installing it from a cd, you pay for access to a website where you use microsoft word in your browser
OR you get a small program that doesn't use much processing power and you use as a microsoft word program, but it uses the internet to communicate with a central server that does the heavy work like spell checking (contrived example)
and
service oriented architecture:
which can be an aspect of the preceding item, but doesn't have to be
it's where there are a bunch of programs running at the same time, and they can make requests of each other for work
so say the spell checking program doesn't have access to a database, it can make a request from another service for it to store your word document
then later it can request a load of that document if you want to open it again (and when you open it at home, you might go straight to that service instead of through the spell-checker one!)
I've tried to explain it in laymens terms, I program SOA applications for a living
