  We present a detailed investigation of the variability of 428 C IV and 235 Si
IV Broad Absorption Line (BAL) troughs identified in multi-epoch observations
of 291 quasars by the Sloan Digital Sky Survey-I/II/III. These observations
primarily sample rest-frame timescales of 1-3 yr over which significant
rearrangement of the BAL wind is expected. We derive a number of observational
results on, e.g., the frequency of BAL variability, the velocity range over
which BAL variability occurs, the primary observed form of BAL-trough
variability, the dependence of BAL variability upon timescale, the frequency of
BAL strengthening vs. weakening, correlations between BAL variability and
BAL-trough profiles, relations between C IV and Si IV BAL variability,
coordinated multi-trough variability, and BAL variations as a function of
quasar properties. We assess implications of these observational results for
quasar winds. Our results support models where most BAL absorption is formed
within an order-of-magnitude of the wind-launching radius, although a
significant minority of BAL troughs may arise on larger scales. We estimate an
average lifetime for a BAL trough along our line-of-sight of a few thousand
years. BAL disappearance and emergence events appear to be extremes of general
BAL variability, rather than being qualitatively distinct phenomena. We derive
the parameters of a random-walk model for BAL EW variability, finding that this
model can acceptably describe some key aspects of EW variability. The
coordinated trough variability of BAL quasars with multiple troughs suggests
that changes in "shielding gas" may play a significant role in driving general
BAL variability.
