There isn't really a good answer to this question. In fact, there is no definitive line between "minor" and "substantial". It simply can't exist—the terms are intentionally subjective and open to interpretation. That's why we allow people to vote on them.
I can give you my opinion, though. I think it's a fairly common opinion, but I can virtually guarantee that there are people who disagree with me. Here are the basic things that will make me reject an edit as "too minor" (or uncheck the "this edit was helpful" box when clicking "Improve"):
- It makes only trivial formatting changes (like adding bold, italics, or inline code formatting) that were either inappropriate and/or not required in order to make the post readable.
- It fails to fix obvious problems with the post (like removing signatures, adding linked images inline, or re-wording incomprehensible titles).
Note that this "too minor"/"substantial" distinction doesn't apply to moderators and users with full edit privileges. They can make as trivial edits as they desire because they don't have to be reviewed by other community members (and therefore, don't waste other people's time with overly trivial edits). Suggested edits are expensive because they require the time, energy, and effort of at least two or three trusted community members. We're happy to give of that time if it positively improves the site, of course, but it grows tiring to have our time wasted by excessively trivial edits that fail to do so.
[Of course, some people have argued that even with full edit privileges, one should generally refrain from making overly trivial edits.
The justification generally centers around the fact that all edits 'bump' the question. I'm not sure that I agree with that, especially on a site as large as Stack Overflow. It might be something to keep in mind on smaller sites, but even there, one or two bumped questions is not a problem—it might even be a good thing. The only time you really want to watch out for this is if you're doing a massive clean-up and run the risk of bumping an excessively large number of questions for trivial edits. In those cases, do the community a favor and space out your edits.
Aside from the bumping issue, and more generally, the fact that you have full edit privileges is an indication that the community trusts your judgment when it comes to making edits. We trust that you'll use your powers for good, to improve the site. We trust that you know what you're doing. We trust that you'll make the right call. There are some times when only a trivial edit needs to be made. There are some times where a small thing can really make a difference, or is really hampering the quality of a post. In those cases, the edit should be made, and we have given you the power to do so.]