A padding oracle attack was possible against TLS CBC ciphersuites because if a certain length check on the packet fields failed, a different alert type than one used for message authentication failure would be returned to the sender. This check triggering would leak information about the value of the padding bytes and could be used to perform iterative decryption.

As with most such oracle attacks, the danger depends on the underlying protocol - HTTP servers are particularly vulnerable. The current analysis suggests that to exploit it an attacker would first have to guess several bytes of plaintext, but again this is quite possible in many situations including HTTP.

External references:

http://botan.randombit.net/security.html