As far as I know:
Wordpress.com is a provider / hoster, who offers WordPress-Accounts on their own server; they have a very limited selection of themes and plugins. Users cant install other plugins/themes on their servers.
If you want to be able to install any plugins and themes, try an “self-hosted wordpress-installation”. You need a webspace-account with php and sql, for a few Euros (or dollar, …) per month.