Why enable automatic improvements?
Automatic improvements allows Google to update the data in your Merchant Center when it finds changes on your site to price and availabilty. It can also improve your images by automatically removing promotional overlays.
Why enable automatic item updates?
Google uses the structured data markup on the website and advanced data extractors to automatically cross check, on a periodic basis, price and availability on the website with price and availability in your product feed. If automatic item updates are disabled, products with mismatched data aren't eligible to appear in Google. If automatic item updates are enabled, and, for example, the price has changed on the website, Google can update the price for the product and therefore avoiding a disapproval.
It is important that your structured data implemention is accurate, as, if not, this can cause Google to change the price to the wrong value.
Why enable automatic image improvements?
Google prohibits promotional overlays in product images. If automatic image improvements are disabled, products with images with promotional overlays aren't eligible to appear in Google. If automatic image improvements are enabled, Google will try to automatically remove overlays and replace the image used in Google. If successful, the product will become eligible to appear in Google; otherwise it will remain ineligible.