pwSafe uses Twofish for encryption. Twofish is a 256-bit algorithm which was one of the five finalists of the AES competition (won by Rijndael algorithm). If you wish more details, that's the technical description of pwSafe's file format.
Since only using strong algorithms is not enough, pwSafe borrows its security code from the Password Safe open-source project, which is around 10 years old and has been originally designed by the security guru Bruce Schneier. By doing that, it ensures a very low probability of having security related bugs which would allow an attacker to go around the cryptography. It also brings another advantage: it is compatible with many apps for many different platforms.
When transfering your safes to and from Dropbox it uses SSL, which encrypts all data and also authenticates the Dropbox server. The same goes for Cloud Backups.
If a master password is configured, when pwSafe is moved to the background, it encrypts the passwords you used to open the safes which are not closed (the ones with a red padlock). This encryption is performed using AES-128 in CBC mode and an encryption key derived from your master password by hashing it and a random salt with SHA-256 128 times.
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