Tabular programming is an alias of Table Oriented Programming paradigm (TOP). For TOP the key concept is a table as for Object Oriented Programming (OOP) the key concept is an object.
In general TOP language, tool, programming etc. deal with tables and focus on them. However a programmer can utilize certain paradigm even in languages that don't support nativly that paradigm. For instance languages that don't have keywords for defining classes and don't support syntax for operating on instances can be used to write object oriented code. For example in C language we can define a struct and put a reference to that struct into a function in order to simulate this pointer and method invocation. However OO code written in C++ or C# will be much more intuitive, compact, legible, flexible and less bug prone.
The Falcon is a language that support TOP nativly in terms that it contains built in programming structures to facilitate dealing with tables. Altough saying that Falcon constitutes TOP is like saying that C++ constitutes OOP. In fact, their are a tool, that facilitates or even enforces certain programming style.
I think, but maybe I'm wrong, that we should seek TOP ideas also in place that is created for operating especialy on tables. SQL Server and Analysis Services are an arena where tabular data focused operations are performed. In particular new Tabular Model Programming uses tables as key elements to deal with. I believe that there will be introduced more intuitive API support for tabular programming in the future. So I let myself to speak about TOP in context of Tabular Model Programming just as an another aspect of TOP beside Falcon.
Tabular Model Programming is used in Analysis Services which belongs to SQL Server Technologies so is closely associated with relational databases and business intelligence. Tabular mode is a new approach for creating a business intelligence semantic model as an alternative to multidimensional mode so it should be compared the latter. Each solution differs in how they are created, used, and deployed. Tabular mode is faster to design, test, and deploy. Is also familiar to audiences who work with relational databases, Excel, or Access. For more details and internals refer to Comparing Tabular and Multidimensional Solutions.
I think that the best way to understand what is a Tabular Model Programming is to use it in practice. Get through Tabular Modeling (Adventure Works Tutorial) and feel it.