If you purchased books for your Sony reader, they are in ePub format, but wrapped with DRM (Digital Rights Management). In order to read those books on any other reader, you would have to "unwrap" the DRM from the file leaving you with an unprotected ePub file that the iBooks app can read.
There is software that will allow you to do this (don't ask me how I know!). You can search for it on Google (or whatever search engine you prefer), but on this forum, we do not allow the discussion of acquiring software by any other means than that intended by the author, owner, developer or publisher and this includes unwrapping the DRM from copyright protected publications.