FileDrop is basically as secure as email itself is. It therefore depends
on the sender's and recipient's email being secure and that the
recipent's do not pass on the information to get to the files to
others they should not. Also remember email is transfered over the
network "in the clear". Anyone with access to the relays and routers
could "listen in".
The emails sent to recepients will contain web address URL's into this site which are themselves the pass keys to getting the files. They are long, randomly generated addresses that are near impossible to guess. Also, they use https so do go over an encrypted channel. But someone only needs to be able to read any of the emails sent to get access to those "keys".
In short, do not use this for truly sensitive information. Don't use regular email either. Contact your sysadmin for help if you need to transfer large files with sensitive info.