If you're using the Babbel app for iOS this is possible. It's not possible if you're accessing your Babbel account at www.babbel.com via a browser.
Please remember to download the courses, lessons, and review items you want to work on before going offline.
Please also be aware that updating your operating system or the Babbel app itself will temporarily delete any previously downloaded items.
You'll find links to the Babbel apps here: www.babbel.com/mobile