Using citric acid as a chelating agent, Bismuth ferrite or BiFeO3 (BFO) nanoparticles have been synthesized by sol-gel method and formation of single phase rhombohedral BFO is confirmed by powder XRD. Three Al and four E modes related to the different sites occupied by Bi atoms are found in Raman spectrum. From HRTEM analysis, the average particle size of the nanoparticles is evaluated as 49 nm. The prominent peaks in DTA at 822 and 980 degrees C reveal alpha-beta (rhombohedral-orthorhombic) and beta-gamma transitions (orthorhombic-cubic) respectively. The thermal conductivity and specific heat have been measured by a photopyroelectric (PPE) thermal wave technique. Transitions due to charge transfer excitation and DMSO-d(6) crystal field excitation of Fe3+ ions have been detected by the UV-Vis DRS and the energy bandgap is 2.05 eV. Nanoparticles exhibit reverse saturable absorption (RSA) in open aperture Z-scan technique (Nd: YAG, 532 nm, 5 ns, 150 mu J) with an optical limiting threshold of 2.44 x 10(13) W/m(2). Frequency and temperature dependent dielectric measurements reveal the ferromagnetic to paramagnetic phase transition at 375 degrees C. Electrical conduction due to small polaron transport with activation energy of 0.581 eV at 1 kHz is confirmed from AC conductivity (sigma(ac)) measurements. Magnetization measurement indicates a weak ferromagnetism with the saturation magnetization (M-s) 1.177 emu/gm and coercive field (H-c) 151 kOe at room temperature. For applied fields 1500-6500 V, saturation polarization (P-r) varies from 0.082 to 1.13 mu C/cm(2) with a corresponding increase of coercive field (E-c) from 2.32 to 23.01 kV/cm. The coexistence of ferroelectric and ferromagnetic orders is confirmed through magneto-electric (M-E) coupling measurement with a M-E coupling coefficient (a) of 0.011 Vcm(-1)Oe(-1).