Comments are directly attached to different types of content, like a post or a page, and are handled through WordPress built-in comment system as default. Not all WordPress themes support them, though. Most themes that support comments also allow visitors to reply to each others comments. Comments with responses are displayed in a nested thread, with the original comment (the one that was responded to) at the top level. Depending on your theme, the comment section of your site might also display pingbacks and trackbacks.
You can view and edit comments on your site by clicking Comments in the left sidebar on the administration panel, and adjust settings for the comments in Settings → Discussion. In the settings, you can select whether comments need to be approved before they are published on the site, if you should get an email notification when a new comment is submitted, and activate and deactivate the comment function for the entire site. As default, each comment must be manually approved before it’s displayed on the site.
You can also activate and deactivate comments for a specific post or page by opening the post/page in the administration panel, clicking the “Screen Settings” in the top right, marking “Discussion” as checked, scrolling down to the bottom of the page and checking/unchecking the “Allow Comments” checkbox.
If you are having problems with comment spam on your website, you can give the spam protection plugin Akismet a try. It is included with every WordPress installation, and its spam filters will prevent most spam comments from getting published on your site.