Vivparous animals have internal fertilisation and the eggs develop inside the mother. The key idea is that the growing embryo gets its nutrition from a placenta in the mother's womb. It is the standard method for all mammals except monotremes.
Those reptiles which do not lay eggs mostly keep soft-shelled eggs inside their bodies. The embryo exists on the material in the egg. They are ovoviviparus, because of the source of nutrition. However, there are some amphibians and a few reptiles which are genuinely viviparous because they get their nutrition direct from the mother.
Viviparous plants produce seeds that germinate before they detach from the parent. In many mangroves, for instance, the seedling germinates and grows under its own energy while still attached to its parent. Then it drops into the water to transport away.
In some trees, like jackfruit, the seeds can be found already germinated while the fruit goes overripe. This condition is not vivipary because the moist and humid conditions just mimics a wet soil. However, the seeds can germinate under soil too.
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Red mangrove seeds germinate while still on the parent tree.
Viviparity Facts for Kids. Kiddle Encyclopedia.