Something customary is done according to practice. When a bride walks down the aisle, it's customary for everyone at the wedding to rise out of respect.
Every culture has its own customary traditions. In American culture it's customary for a child who loses a tooth to put it under her pillow and wait for the Tooth Fairy to arrive. In Greece, on the other hand, it's customary to throw a child's lost tooth onto the roof for good luck. Customary can also reference habitual things a person does, like taking your shoes off when you come home, or writing in your diary before bed.