It's commonly used to emphasize a point or opinion, similar to the English phrase "and I'm telling you!"
For example:
* "K yo digo que esta película es muy buena." (And I tell you this movie is very good.)
* "No, no, k yo digo que no te preocupes." (No, no, and I say don't worry.)
The "k" is a slang abbreviation of "que," which means "that." So, the phrase is essentially a shortened version of "que yo digo."