A worldline is the history of a particle as represented on a space-time (Minkowski) diagram. The world-line of a particle is straight if the particle moves uniformly and is curved if it moves non-uniformly (i.e. if there is an acceleration). Rays of light can be treated as the worldlines of photons. The worldlines of particles under the influence of a gravitational field are geodesics in space-time. The world-line of a photon near a star, such as the Sun, is slightly bent due to the light being deflected by the gravitational field of the Sun.
My Worldline is the title of the autobiography of George Gamow, the Ukrainian-American physicist.