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
Native speaker here, and as most of you are saying the thing with mentioning that your are sitting, standing, lying etc. is uses for emphazising that you are doing it right now. You would for example say "Jeg sidder og spiser" if someone is asking you something like "Er du klar til at gå?" (Are you ready to go?) but are in the middle of your meal and want to emphazise that you are not ready YET.