If we use the culinary world as a comparison, proofreading is the plating. Great chefs want the ingredients they use to be of the highest quality and they want it to taste scrumptious, but they also want to present their finished plate in the most clean and beautiful way.
This is where proofreading comes in. Where editing would be about the ingredients of your manuscript, proofreading is about presentation.
Spell check is not enough. The English language is just too complicated for a single computer program to be able to catch every typo, misspelled word, or grammar mistake.
A good proofreading of your manuscript should be the last step you take before submitting your work for publication.