Current versions of WordPress come with Akismet installed by default. Akismet uses a unique algorithm combined with a community-created database to "learn" which comments are comment spam and which are legitimate.
Of course, if the problem isn't spam, you can disable comments via Discussions.
In your Dashboard, go to either Pages or Posts, locate the one you want to edit, and click on its title. Then, locate the Discussion module on the edit screen and to prevent any kind of discussion and comment, uncheck both boxes.