It automatically renames your media filenames depending on their titles. When files are renamed, the references to it are also updated (posts, pages, custom types and their metadata). If you have the Pro version, this can be done also based on the title of the post (page or any other custom type) the media is attached to.
The Pro users are given a few more features like manual renaming, renaming depending on the post the media is attached to, logging of SQL queries and a few more options. With the Pro, a good process is to actually let the plugin do the renaming automatically (like in the free version) and to do manual renaming for the files that require fine tuning.
For more information about Media File Renamer, check the official page about it: Media File Renamer.
Discounts are generally not offered but if you are a happy user of the free version and want to help us in promoting the plugin (on social networks, in a blog post, etc), please contact us.