worldwide
= For the whole internet
non-exclusive
= You can still license your stuff to others
royalty-free
= Dropbox doesn't have to pay you for this license
sublicenseable
= The license you grant Dropbox can be transferred to other companies, in the event of a company merger or similar
rights to use
= Doesn't mean anything
copy
= So they can copy your files between their internal servers
distribute
= So that they can distribute your public files to other users
prepare derivative works of
= So they can create thumbnails, extracts, previews etc
perform
= Doesn't mean anything
or publicly display
= List your public files to others
But it doesn't say public files. They ask for that privilege for all files and then leave it to vaguely worded clarification in the privacy policy.
They don't have to plan something "sinister", but boundaries are pushed slowly. This sounds to me like a first step, and disregard for privacy.