"A Bitcoin implementation that does not verify everything, but instead relies on either connecting to a trusted node, or puts its faith in high difficulty as a proxy for proof of validity. BitCoinJ is an implementation of this mode."
I'm not sure about how backups work as I never tested the wallet but people don't use that wallet anymore , instead, Mycelium is probably the best choice : https://play.google.com/store/apps/details?id=com.mycelium.wallet
It doesn't need to download the blockchain either and you could make backups just by backing the master seed (see the full list on features in the link of Google play - more features are coming in the upcoming days/weeks probably)
Thanks for reply!