Gravitational energy is the energy source of many astrophysical systems in the universe, such as quasar and X-ray binaries, etc, and accretion is an effective mechanism of releasing gravitational energy.By the study of accretion disc, people can explain many phenomena on observation, such as luminosity and radiation spectrtum, etc.Accretion has become an effective tool for people to understand a variety of high energy phenomena in the universe.　　The first chapter of this thesis briefly reviews the current situation and progress of the theory of black hole accretion disc.Three successful accretion models, namely the standard thin disc (SSD), the slim disc and the ADAF, are briefly introduced.We concentrate our attention on the ADAF model, which has become hot in the domain of accretion in recent years, and give the self-similar solutions, global solutions and application of ADAF model.　　We study the quasar optical variability using accretion disc model in chapter two. Some different correlations between optical-ultraviolet (UV) variability and other quasar properties, such as luminosity, black hole mass and rest-frame wavelength, were discovered.The positive correlation between optical-UV variability amplitude and black hole mass was first found by Wold et al.(2007), and this was confirmed by Wilhite et al (2008).We suggest that the accretion disc model can explain these correlations, provided the optical-UV variability is triggered by the change of accretion rate.The disc temperature of accretion discs decreases with increasing black hole mass, which leads to systematical spectral shape difference with black hole mass even if the black hole is accreting at the same rate m (m =M/M Edd).The observed positive correlation between optical-UV variability and black hole mass can be well reproduced by our model calculations, if the mean accretion rate m0～ 0.1 with variation ofδm～ 0.4-0.5 m0.We also found that the observed correlations of optical-UV variability amplitude with luminosity or rest-frame wavelength can be qualitatively explained by this accretion disc model.　　In the third chapter we study the global dynamics of advection-dominated　　accretion flows (ADAFs) with magnetically driven outflows.A fraction of gases in the accretion flow is accelerated into the outflows, which leads to decreasing of the mass accretion rate in the accretion flow towards the black hole.We find that the r-dependent mass accretion rate is close to a power-law one, m∝ r s, as assumed in the advection-dominated inflow-outflow solution (ADIOS), in the outer region of the ADAF, while it deviates significantly from the power-law r-dependent accretion rate in the inner region of the ADAF.It is found that the structure of the ADAF is significantly changed in the presence of the outflows.The temperatures of the ions and electrons in the ADAF decreases in the presence of outflows, as a fraction of gravitational power released in the ADAF is tapped to accelerate the outflows.