Motion detection and direction recognition are two important fundamental visual functions among the many cognitive functions performed by the human visual system. The retina and visual cortex are indispensable for composing the visual nervous system. The retina is responsible for transmitting electrical signals converted from light signals to the visual cortex of the brain. We propose a photonic spiking neural network (SNN) based on vertical-cavity surface-emitting lasers with an embedding saturable absorber (VCSELs-SA) with temporal integration effects, and demonstrate that the motion detection and direction recognition tasks can be solved by mimicking the visual nervous system. Simulation results reveal that the proposed photonic SNN with a modified supervised algorithm combining the tempotron and the STDP rule can correctly detect the motion and recognize the direction angles, and is robust to time jitter and the current difference between VCSEL-SAs. The proposed approach adopts a low-power photonic neuromorphic system for real-time information processing, which provides theoretical support for the large-scale application of hardware photonic SNN in the future.