We explore the variability of quasars in the MgII and Hbeta broad emission lines and UV/optical continuum emission using the Sloan Digital Sky Survey Reverberation Mapping project (SDSS-RM). This is the largest spectroscopic study of quasar variability to date: our study includes 29 spectroscopic epochs from SDSS-RM over $6$ months, containing 357 quasars with MgII and 41 quasars with Hbeta . On longer timescales, the study is also supplemented with two-epoch data from SDSS-I/II. The SDSS-I/II data include an additional $2854$ quasars with MgII and 572 quasars with Hbeta. The MgII emission line is significantly variable ($Delta f/f$ 10% on 100-day timescales), a necessary prerequisite for its use for reverberation mapping studies. The data also confirm that continuum variability increases with timescale and decreases with luminosity, and the continuum light curves are consistent with a damped random-walk model on rest-frame timescales of $gtrsim 5$ days. We compare the emission-line and continuum variability to investigate the structure of the broad-line region. Broad-line variability shows a shallower increase with timescale compared to the continuum emission, demonstrating that the broad-line transfer function is not a $delta$-function. Hbeta is more variable than MgII (roughly by a factor of $1.5$), suggesting different excitation mechanisms, optical depths and/or geometrical configuration for each emission line. The ensemble spectroscopic variability measurements enabled by the SDSS-RM project have important consequences for future studies of reverberation mapping and black hole mass estimation of $1<z<2$ quasars.
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