Quick Connect and Active Roles Synchronization Service mappings are designed as a 1:1 (one-to-one) relationship between a source object and a target object.
These mappings are what allows the service to know which object in a source is to be synchronized to which object in a target.
If it happens that there is more than one object on a single side (source or target) that has the same value for a mapped attribute, this is seen as a duplicate object. This causes the service to be unable to determine which of the two objects is the correct object to synchronize. When this occurs, your are met with an Ambiguity Error.
When met with an Ambiguity Error, you can view the object that is affected by this. With knowing the mapped attribute being used, you can search for that in Active Directory or the target system to find the duplicate objects. Take appropriate action to dissolve the duplicate, either by changing the value for one object or removing one object.
Once the duplicate is taken care of, the Ambiguity Error will go away and a mapping will be successful.