"katha" ,in this context, means a philosophical debate. Sri Madhvacharya has defined 'katha' as of three types. they are called 'vada', 'jalpa'  and 'vittanda'.

Vadakatha: It is a discussion between a 'guru' and a 'sishya' on any

philosophical topic during or after a lesson. It is a healthy discussion intended for the benifit of the student. A student is free to discuss with the 'guru' and even argue if he differs from him , but has to accept the decision given by the ' guru', politeness and respect for the teacher being observed strictly.

jalpakatha:  this is a discussion of a topic of philosopy between two

scholars of different schools of thought, or betweeen any two persons who have divergent views. The discussion is held with a third party as the judge on a public platform.  Srimadacharya has dealt with in detail the nature of such discussion, selection of  judges etc.

vittanda:  This is a discussion more like 'jalpa'. But when one of the

parties is losing, if he resorts  to talking without 'pramanas' or  making personal comments other party and may make comments in a rough language the debate is called 'vittanda'.

These two works of Srimadacharya are unique in the field of shastraic

thought.   

' yO vipralambha viparItamatiprabhutAn vadAnnirasya nikhilAn bhuvi tattvavadam sarveshvarO Haririti pratipAdayantam Anandateertha munivaryamaham namAmi'