What is lomdus?

I have been thinking of writing a post on this for awhile. For those who are "holding in learning" the pinnacle of achievement is being considered a "lamdan". Most high level yeshiva shiurim are devoted to "lomdus", especially of the variety commonly known as the "Brisker derech". So what is lomdus and what difference does it make to how you learn?
Rather than start with a definition, I want to start with an example. A person became an onein and was exempt from havdalah on Motzei Shabbos - would this person have to make havdalah on Sunday after the meis is buried? The R"I compares this case to that of a lame person who is exempt from aliya l'regel on the first day of Yom Tov. A person who has an obligation to offer an olas r'iya on the first day may fulfill that obligation during the duration of the week of Yom Tov; however, one who is exempt on the first day is exempt for the entire duration. Similarly, even though if one has no wine on motzei shabbos one can make up havdalah the next day, the onein had no obligation of havdalah on motzei shabbos and is therefore under no obligation to do so on the next day. The MaHaRaM Rotenberg, however, disagrees and holds that once the meis is buried on Sunday, the obligation of havdalah must be fulfilled.
Before "lomdus" became the rage, out story would just about be over. We have a difference opinion in Rishonim regarding a specific case in halacha. We can go a step further and ask why the R"M M'Rotenberg disagrees with the argument of the R"I. and here is where the pandora's box is opened.... think about it, and I'll be back with more : )