Where does the 'extra' data come from when transcoding video?
When video or audio data is compressed, it works by two different mechanisms.  The first (which is the only one used by lossless compression) is to look for patterns that are repeated.  When patterns are found, it can store the data once and reference the stored copy.  

The second is only used lossy compression and involves discarding the least significant parts of the information.  This can be done in several creative ways such as being more forgiving in what pattern can be matched, but the loss of information generally ends up equating to a slight loss of detail.

You can think of it kind of like blurring a photo.  You still have just as many pixels and just as much "raw" data, but the amount of detail stored in that data is reduced, and thus it can be compressed further because it fits patterns better.  When you move from the high compression, lossy format to a lossless format, a large number of those savings are no longer applied, so it stores the raw "but fudged" data again under a new system that isn't capable of as much compression.

Basically the video is uncompressed from your original format to form a file of 1920 by 1080 pixels (assuming it's a 1080p file anyway) and then it is recompressed differently to become a ProRes file.  The file size is large because the ways that it will try to simplify the file are simpler, but the information that is recorded is still the blurred copy that resulted from decompressing the smaller file.

This is also why it is important to work with the highest possible quality files until final output because repeated recompression of files will result in additional quality loss every time.