What type of encryption does Managed Backup use to secure the data being backed up? How secure is my data?

Managed Backup uses the Blowfish encryption algorithm. You can get more information about blowfish algorithm.

Excerpts from the blowfish website:
“Blowfish was designed in 1993 by Bruce Schneier as a fast, free alternative to existing encryption algorithms. Since then it has been analyzed considerably, and it is slowly gaining acceptance as a strong encryption algorithm”.
Managed Backup will support other encryption algorithms as options in the future. As such your data is very secure as blowfish based encryption has never been broken before.