The Gantry Framework is something that controls aspects of your Joomla! template. Stuff like how many columns to show in the homepage, which module positions will appear on mobile etc. You can't create content with Gantry, you simply control the layout of your site's template.

K2 on the other hand is a Joomla! extension for managing content. Think of it a super-charged version of the default content management utility of Joomla!. K2 sits "in parallel" to Joomla's content articles, they don't relate to each other. If you write an article in Joomla, you only get to add a title, your article's body, select the category it belongs, the author and add some tags (if you are in Joomla 3.x). With K2, you have all that plus the option to have an "article image" which is autoresized upon upload to fit your content, you can have image galleries, videos, attachments, additional form fields per category or globally (called "extra fields") and lots more, like better content organization and presentation, more control of what is shown in the frontend per category or per tag etc. etc.

Consider K2 as a content management system within Joomla.

For more, I suggest you follow the 10-part video tutorial here: getk2.org/documentation/k2class2012

Welcome to the K2 Community! :)