Directly from the "save as" menu option:
Copy and trim media with project
Allows all media files that the project is using to be copied into the same folder as the project file. This makes it easier to collect all of the project assets in a single location.
I find it far better to arrange things properly before editing. I create a new directory for each project and put everything i'm going to use for the project in that folder, including .veg files. When the project is done i back up that folder and it's all together.
I way prefer this over the "save media" option as it doesn't modify the files or change their names. It's also just a good housekeeping habit to get into in any case.