If I understand correctly, this contruction is used to emphasize that it is right now that I am eating. In contrast, in English, we use the progressive "ing" form of verb constantly, even when there is no implied emphasis, where most languages would simply use a regular present tense.
English have a time more then danish have. In danish we don't have the time, the -ingform represents (i hope this makes sense) so you cant really translate it directly. We Danes have a habit of putting -ing bminto every english sentence because it sounds more english to us So: Jeg sidder og spiser I sit and eat I am sitting and eating It means the same in danish