Seizures induced by stroboscopic lights are an example of reflex seizures. This type of epilepsy includes seizures evoked by touch and movements as well. The mechanism behind generalized reflex seizures (generalized epilepsy, as opposed to partial epilepsies, is accompanied by a loss of consciousness) was abstracted nicely by Ferlazzo et al, 2005:
Patients with  generalized reflex seizures appear to have regions of cortical hyperexcitability overlapping or coinciding with areas physiologically activated
during specific sensory stimulations and cognitive or motor activities. When these areas receive appropriate afferent volleys and a critical mass of cortex is activated,
an epileptic activity is produced that ultimately involves cortico-reticular or cortico-cortical pathways resulting in a generalized or bilateral epileptic event.
In other words, stimuli such as stroboscopic light evoke activity in sensory cortex. If the area of excitation is large enough and occurs in a region of the brain that has an epileptic focus (hyperexcitable cortex) than it may trigger a seizure characterized by an uncontrolled wave of activity spreading across the cortex.
Specifically for flashing-light induced seizures it is thought that seizures start in the visual cortex in the occipital lobe due to impaired cortical mechanisms of contrast gain control for certain visual patterns, producing an abnormal excitatory response to patterns of relatively low temporal frequency and high luminance contrast. Specifically, the seizures may be caused by a loss of control over high-frequency oscillatory processes that normally operate transiently to connect the involved neural assemblies. Generalized seizures can occur if normal excitation of visual cortex involves a ‘critical mass’ of synchronized activity in a cortical area with synchronization and subsequent spreading of excitation from the occipital lobe trigger zone (Parra et al, 2005).