We present new results for the three-point correlation function, ζ, measured as a function of scale, luminosity and colour from the final version of the 2dF Galaxy Redshift Survey (2dFGRS). The reduced three-point correlation function, Q3~ζ/ξ2, is estimated for different triangle shapes and sizes, employing a full covariance analysis. The form of Q3 is consistent with the expectations for the Λ cold dark matter model, confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on Gaussian primordial fluctuations. However, we find a clear offset in amplitude between Q3 for galaxies and the predictions for the dark matter. We are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9σ level. On weakly non-linear scales, we can interpret our results in terms of galaxy bias parameters. We find a linear bias term that is consistent with unity, b1= 0.93+0.10-0.08 and a quadratic bias c2=b2/b1=-0.34+0.11-0.08. This is the first significant detection of a non-zero quadratic bias, indicating a small but important non-gravitational contribution to the three-point function. Our estimate of the linear bias from the three-point function is independent of the normalization of underlying density fluctuations, so we can combine this with the measurement of the power spectrum of 2dFGRS galaxies to constrain the amplitude of matter fluctuations. We find that the rms linear theory variance in spheres of radius 8 h−1 Mpc is σ8= 0.88+0.12-0.10, providing an independent confirmation of values derived from other techniques. On non-linear scales, where ξ > 1, we find that Q3 has a strong dependence on scale, colour and luminosit
