According to the Torah, the mitzvah of lulav is only on the first day of Sukkot, except in the Temple, where it applies all seven days. After the destruction, the rabbis decreed that we take the lulav all seven days, everywhere, as a remembrance to the Temple.
On various occasions throughout our lives we remember the Temple in other ways: fasting on Tisha Beav, breaking a glass at weddings, leaving part of one's house unpainted, avoiding singing and music in certain situations, and so on. Lulav appears to be odd company for these mournful customs. How can they all be classified as remembrances of the same thing?
It appears that there are two very different ways in which we remember the Temple. Tisha Beav is a remembrance of the catastrophe of destruction. Lulav, on the other hand, is a remembrance of the Temple as it was when it stood. Here we remember not the disaster of the past, but the glory of the past. This remembrance should engender not sadness but pride and joy.
Chazal wanted the joy a Jew would experience in the Temple, the overwhelming inspiration with which Temple visitors would be overcome, to continue even after the destruction. The great experience of standing before God would therefore be perpetuated throughout the generations. This is the goal of our lulav-waving on the last 6 days of Sukkot - perhaps differing from our goal on the first day.
(R' Soloveitchik, 1969)
[I would add: this, like Pesach and Yom Kippur mussaf and sukkah and who knows what else, seems to be an example of reenactment and re-living in addition to simply remembering.]
[I originally thought this contradicted my discussion of lulav from last year, but on second thought, what I wrote could accurately describe what happened in the Temple. For us today outside the Temple, the added aspect of remembrance would add complexity and create room for disagreement.]