Binary classfication vs One-class classification
Binary classification is needed when requirement is to capture data into two classes. if you can't capture data in two classes where you need only one you go for One-class.
you can check this link for better explanation 
http://rvlasveld.github.io/blog/2013/07/12/introduction-to-one-class-support-vector-machines/

If you take binary classification, svm tries to find best possible space between A and B. If there is only one class A model tries to create a boundary around it and classify. Take for example patient disease classification: For +ve some symptoms t1, t2, t3, t4, t5 for -ve he has t1, t2, t7. in the above case it is difficult to classify using one class because model classifies patient having t1, t2 as +ve because of proximity to +ve class. The second label gives you more info for better classification.