Hi,
If you don't embed the images in the emails, the receiver will still be able to see the images in the email by just clicking on the button of his email client to display the images. If you embed the images, then it is not necessary for the receiver to click on anything to see the images in the email, but some email server, like apparently yours, cannot handle embedded images, either because of a restriction in their configuration, no support for it, or because the images are too big to be embedded in the emails that the email server is trying to send.
I would recommend that you contact your hosting company (which is usually providing your web server with the email sending capability via its own email servers) so that they can tell you what's going on with the embedded images in your emails.
On our end, there is not much we can do as HikaShop is only telling your email server (via the Joomla library) to send the emails with the images embedded or not, but it's then up to it to actually send the emails.