Based on my experience with corporate terms and conditions, when a term is capitalized (as "Prior Agreements" here), it is defined somewhere; usually at the beginning of the Ts & Cs. Are you sure that it is not defined? Perhaps you don't have the complete text.
But -- as you said -- the precise meaning doesn't appear to be relevant. But what is relevant is that these "Prior Agreements" have at least two components: (1) they impose some conditions on the Assignor, and (2) they convey some benefits to the Assignor.
What the OP says, in effect, is that the Assignor (1) imposes upon the Assignee all the conditions of the "Prior Agreements" that had previously been imposed on the Assignor; and also (2) conveys to the Assignee all the benefits that these "Prior Agreements" had previously conveyed to the Assignor.
(But ... I'm no lawyer; this is just my layman's understanding of legalese.)