We investigate the optical variability of 7658 quasars from SDSS Stripe 82. Taking advantage of a larger sample and relatively more data points for each quasar, we estimate variability amplitudes and divide the sample into small bins of redshift, rest-frame wavelength, black hole mass, Eddington ratio, and bolometric luminosity, respectively, to investigate the relationships between variability and these parameters. An anti-correlation between variability and rest-frame wavelength is found. The variability amplitude of radio-quiet quasars shows almost no cosmological evolution, but that of radio-loud ones may weakly anti-correlate with redshift. In addition, variability increases as either luminosity or Eddington ratio decreases. However, the relationship between variability and black hole mass is uncertain; it is negative when the influence of Eddington ratio is excluded, but positive when the influence of luminosity is excluded. The intrinsic distribution of variability amplitudes for radio-loud and radio-quiet quasars are different. Both radio-loud and radio-quiet quasars exhibit a bluer-when-brighter chromatism. Assuming that quasar variability is caused by variations of accretion rate, the Shakura-Sunyaev disk model can reproduce the tendencies of observed correlations between variability and rest-frame wavelength, luminosity as well as Eddington ratio, supporting that changes of accretion rate play an important role in producing the observed optical variability. However, the predicted positive correlation between variability and black hole mass seems to be inconsistent with the observed negative correlation between them in small bins of Eddington ratio, which suggests that other physical mechanisms may still need to be considered in modifying the simple accretion disk model.