If you are wondering what are those profiles are about and how they are related to the well-adopted BP1.0, read . As the chair of the WS-I Basic profile working group, Chris Ferris of IBM explains in  why we need the three profiles, how they are supposed to be used, and what has been changed since BP1.1.
In a nutshell, in the new release, Basic Profile has been re-architected to enable the composition of profiles that support multiple bindings such as SOAP over HTTP, SOAP Messages with Attachments over HTTP, and eventually MTOM/XOP over HTTP. In the new architecture, binding independant requirements are kept in BP1.1 while binding-specific requirements have been separated into their own profiles (in this case SSBP1.0 and AP1.0, more might be defined in future), each with its own conformance claim.
Correspondingly the WS-I testing tools have also been modified to enable composition of the Test Assertion Documents (TAD) such that conformance to a set of relevant profiles can be measured. Basically, if your Web service is not using attachments, then you would use the TAD composition of BP1.1 plus SSBP1.0 to test conformance. If you are using attachments, then you would use the TAD composition of BP1.1 plus AP1.0.
Note also that Web services that use an alternate binding for SOAP, such as SOAP over FTP, JMS, or MQ, can now use the BP1.1 stand-alone to assess conformance, which was not possible with BP1.0 because of the requirement to use SOAP/HTTP binding.