Taga Shrine is a holy site where religious souls gather to pray. You can do the same, or respectfully observe others as they worship.
This Taga sacred place is a good place to start your day of sightseeing. There's plenty to see nearby, like Hikone Castle, Ryotanji Temple, and Sawayama Castle Ruins. Wander around at your leisure at Taga Shrine before heading to these other fine sights.