Most LAMP (Linux Apache Mysql Php) hosts meet the minimum requirements to run BEdita. However BEdita can easily be installed also on other platforms like Windows or OSX, for example.
Just be sure that your host environment web server, database server and php are compatible with the version of BEdita you want to install.
BEdita 3.4 corylus - minimum requirements
(**) other web server like Nginx or Microsoft IIS should work but are not officially supported