Buddha Statues came into existence several hundred years after the Buddha passed away. Before the introduction of figures, Buddhists offered flowers, oil lamps, and incense in reverence of The Buddha statues to Buddha relics placed inside a Stupa or Pagoda. But Buddha relics were very, very rare, and only a handful of Asian countries had possession of them. Hence, only a limited number of Stupas/Pagodas were building. Probably that was one reason for creating Buddha statues; because with Buddha Statues, it would be possible for a Buddhist to construct a Buddha Shrine in a public area or even in a home and pay homage to the Buddha; without relics.
Another reason could be: The Buddha-nature is in the Buddhist scriptures, which were in Pali language (before they translated into other languages), and most people were unable to read Pali (even to date).
Buddha Statues And Stories
As the saying goes,“ A picture speaks a thousand words,” a person can understand the serenity of The Buddha by just looking at a Buddha statue; without reading the Buddhist Scriptures.
Another point is that The Buddha statues created according to the imagination of the artists. That is, Buddha statues in various countries have different facial features. A Chinese Buddha statue has Chinese facial features, and some have big bellies too. It is an understanding among Chinese people( as I have heard) that a big belly is a sign of happiness and prosperity. Japanese, Thai, and Indian/Sri Lankan Buddha Statues have facial features similar to the ordinary people of those countries.
However, there are specific parameters in creating a Buddha statue. The postures are limited to three: Meditating, Resting (horizontally), and Standing. What we see around the world is mostly in the Meditating Posture.
Nevertheless, the Buddha never encouraged in his teachings to create models and pay homage to him. The Buddhists are doing it anyway out of respect for HIM. The following incident mentioned in the Buddhist scriptures will emphasize on how Buddhists should pay respect to the Buddha.
Once a monk who resided in a cave in the forest kept a wooden Buddha statue to worship the Buddha. After nightfall, he would light a wood fire inside the cave to keep himself warm and also to keep animals away from the cave. By the light emitted from the lamp, he would stare at the Buddha statue and mentally focus on the virtues and wisdom of The Buddha for several hours. After that, he would start to meditate on the impermanence of all composite things. This went on for many years. One day after staring at The Buddha statue for about an hour, he got up, went to the figure, picked it up, chopped it into small pieces and put it in the fire, and continued to meditate.