All websites are stored on web servers. A server is just a regular computer, typically with lots of storage. The technicalities vary a lot -- some use lots of cheap regular computers all linked up, some buy expensive servers.
A company owns a data centre somewhere, which is just a large space setup for servers to be stored in, with fast internet connections and air conditioning, as well as uninterruptible power supplies and even backup generators.
They then re-sell the space to a web hosting company that's in charge of their servers and buys them to fit inside the data centre.
This web host then splits the servers up so lots of people use a single server, which they charge people for, such as answerbank.
If the site is a large site, with lots of visitors, they'll want their own dedicated server. If it's even larger, they'll want several servers all to their own. If they're even larger, they'll have several servers in several data centres (we say they're "co-located"), to spread the load and make the site load faster. Huge sites like Google have thousands of servers and buy their own data centres.
This server then runs some stable operating system (sometimes a server version of Windows, but more often some *nix variant such as freeBSD. The cool kids are trying out Solaris, for cool technologies like ZFS.
This then runs web server programs, such as Apache, as well as database software such as mySQL. Programming languages such as Python or PhP are added so that someone like theanswerbank can create a website 'backend' (the clever stuff that sorts all the answers and does all the hard work, but which the visitors like ourselves don't see), which in turn delivers the 'frontend' of the website, which is all the pretty images and things that we see that makes up the site.