The resize settings allow you to save tremendous amounts of disk space. These settings aren't necessarily intended to speed up your site otherwise.
If you're not resizing your images to the correct size pre-upload, this can save you loads of disk space, and help make sure you aren't delivering poster-sized images to mobile devices. A width between 1920 and 2560 is recommend, as that is about the largest you would need for a full-screen display. You can set one of the dimensions to 0 if you only want to limit your images in one direction. To prevent an image from being resized, regardless of the dimensions, insert the string 'noresize' into the filename before upload.
Note: the following settings are available by enabling Ludicrous Mode.
This feature is a tool for site admins to find images on their site that are more than 150% the dimensions that are being displayed within the page. The feature is only visible for admin users, and will highlight any over-sized images with a blue/teal and black border. You can safely leave it enabled to help you track down images that need resizing, and it will have no impact on what your visitors see.
Resize Existing Images
If you have a lot of images already and want those to be resized too, you can check this next box to make sure the bulk optimizer resizes them.
Resize Other Images
As you might have already figured out, normally the plugin only resizes images that get uploaded to the "official" Media Library. But what if you have a plugin that lets you upload images, and it isn't using the Media Library? There are a lot of these, some gallery plugins, webform plugins, or plugins related to BuddyPress and WP Symposium. So, if you want the plugin to scale down those images according to the dimensions you've specified, you need this option. Now, the plugin can't hook into every uploader out there to do this automatically, but you can use the Bulk Optimizer or Scheduled Optimizer to track down those images and get them scaled down to reasonable dimensions. That said, other plugins can take advantage of the EWWW IO resizing by simply using the ewww_image_optimizer_resize_upload( $filename ) function.
A feature that can help save time (and resources) is the ability to disable the resizes that are created by WordPress. Some sites have as many as 20 resizes listed here, so it can be beneficial to look through these and see if you need these to be created or optimized. With WordPress 4.7+ this also applies to PDF preview images. You can disable all PDF previews by disabling the full-size preview image, since that image is used to build all the smaller thumbnails.