I just tried to edit a question with poor spelling and no punctuation. Why does this require an edit summary? I believe I have seen edits without edit summary. Does this have something to do with my low reputation so I can't edit without posting a summary?
You can only submit edits without providing a summary when you have full editing privileges (i.e. at 2,000 reputation). So yes, you have to enter a summary.
We require you to enter a summary for several reasons. First of all, working your way towards the full edit privileges you should develop a habit of always describing what you change. This is especially important for anything that isn't a simple copyedit (and the summary can arguably be left out there), but for example when you change a part of the answer or correct a mistake.
Your reviewers will have to evaluate your edit, and giving them a proper description of what you did puts them into the right mindset. As a reviewer, you don't want to see: "removed 20 characters; added 30 characters", or "I improved the post"—because that's a little obvious—but instead a specific reason of why you chose to edit the post, e.g. "there was a typo in the foo command". This also makes it easier to reject an invalid edit. I remember seeing edit summaries like "this worked for me, thanks" or similar.
Finally, the edit summary is also clearly visible to the original author of the post, as they're notified of any revisions to their own questions or answers. As a courtesy to the author, you should tell them what you changed. Ideally, by telling a new user that you corrected their code formatting, capitalized their "i"s, or that a "MAC" is not the same as a "Mac", you achieve some kind of learning effect without having to add an extra comment to the post.
Of course, if it's just a copyedit, you can just enter "spelling, punctuation" and be done with it. No need to get creative there.