Brainscape maintains several instances of our own backups of our entire database. If there is ever a catastrophic event that causes data loss (e.g. a hack, a server crash, etc.), we will be able to backup our database to the minute. You should be able to fully trust us to maintain your data on our servers.
[Note: We have never actually had to use our backups -- knock on wood -- but it's good to know that they are there.]
That said, some users understandably still feel more comfortable having their own backups, since they have invested so much time creating flashcards. To download your own backups, you can click the menu icon next to the Class title on the website (on your My Classes screen), and choose the Export .CSV option.
This will generate files that you can open in Excel and -- if necessary -- re-upload to Brainscape or another flashcard platform at a later date.
[See also: Can I retrieve Decks that I deleted?]