Those are explained by Kier in the HYS video here. The relevant part starts around the 2:30 mark.
They're intended to help suppress insecure content messages when users post picture URLs and links to sites that don't use SSL. But, they're also handy for tracking outbound links and what pictures are posted on the forum and how many times each has been viewed.
Speaking as someone who runs XF on SSL and previously had to deal with insecure content messages, those are my very favorite XF features. Just a wonderful addition to the core.
Does the default settings in the latest 1.4 build of: image proxy ticked; and "0" days, mean that hot linked images from other sites get saved on the server? This is what I'd like to happen on my sites due to the X image syndrome.