To add to Christiaan's answer, the length of the hair cells also changes along the basilar membrane. They are longer and floppier near the apex. There are many levels of mechanical interaction occurring--the basilar membrane vibrates, the outer hair cells change length and articulate with the tectorial membrane which is also moving, the displacement of the fluid beneath the tectorial membrane causes inner hair cells to depolarize, etc.
Also, if you're asking for an ultimate 'why,' high frequencies are more quickly attenuated so it would make sense for them to be represented at the base, right at the point of transduction from the middle ear. Interestingly, I believe the cochlea grows out from that point during development (e.g. the apex moves out/up/around) but low frequency hearing is the first to mature.
Edited to add sources:
Change in length of hair cells, see table 2: http://upcommons.upc.edu/bitstream/handle/2117/26076/MorellUltrastructure2014_final+proof.pdf;jsessionid=82346B40F24139DA94D7217DCA227C18?sequence=9
Discussion of attenuation by frequency: https://physics.stackexchange.com/questions/87751/do-low-frequency-sounds-really-carry-longer-distances
Cochlear growth: http://onlinelibrary.wiley.com/doi/10.1002/dvdy.10500/pdf