Preparation is key to having a meaningful Seder (and to many other things too. If you keep Shabbat, you don’t start preparing for it ten minutes before candle-lighting time).
Consequently, there is an old custom to the Great Shabbat, to reacquaint ourselves with the ideas and practices of the Seder (Rama, Orach Chaim 430:1).
For the same reasons, before regular synagogue sermons became standard, the Shabbat Hagadol sermon was one of just two annual Shabbat sermons.
The other time the rabbi spoke was on Shabbat Shuvah. (Did someone subversively say “those were the days?”) The topics were the halachot and the broader meaning of Pesach.
This special status was one of the reasons for the name Shabbat Hagadol of the Shabbat before Pesach.
The term became popular in the Middle Ages. Some also point to the words of the haftarah reading for this Shabbat as the source of its name, “Behold, I will send you Elijah the prophet before the coming of the great (hagadol) and awesome day of the Lord” (Malachi 3:23).