I came accross the term Modular Extension as a requirement of an application of I am developing. Any body know what a Modular Extension is all about?
In general, if something is modular it means it's independent to the rest of your application, so that you can switch it on or off as needed, or remove it entirely, without affecting other things.
If something is an extension it means it's not considered a core part of your application, but rather separate functionality that can be developed on its own. Usually, the ability to write extensions implies a relatively well thought-out design and a sophisticated API that allows outside clients to get at the relevant internals of your core application.
Otherwise, though, your question is a little too generic to give a precise answer without more information.
Most probably your employer is trying to tell you that:
They want the application to be easily extended afterwards
They don't want to depend on you forever
They want to deploy (sell) different versions (in terms of enabled functionalities) through simple means (turning modules on/off)
I might mention that all the above points (and much more!) are totally valid business points and there is absolutely nothing wrong with them but for some arcane reason employers are reluctant to express them the way I did.