A "bog" is a muddy swamp. So you can imagine that "getting bogged down" in details is like getting stuck in the mud. If you talk too much about the details of something, you won't move forward with more important discussions.
You don't always have to use the word "details" when you talk about "getting bogged down". You can also give examples of the kind of details that you want to avoid: For example, you could say this when giving someone advice on how to write an essay for a History class:
Try not to get too bogged down in the names of historical figures and the dates when events happened. Focus on why they happened.