What is the term for plants that bloom year after year?

The term for plants that bloom year after year is "perennials." Perennials are plants that live for multiple years, often flowering and producing seeds over those years. They typically die back in response to seasonal changes but regenerate each growing season from their root systems or underground bulbs.

In contrast, annuals complete their life cycle within one growing season. They grow, bloom, produce seeds, and die all in the same year. Biennials have a two-year life cycle, usually growing leaves in the first year and flowering in the second. Deciduous refers to trees or shrubs that lose their leaves seasonally; it is not a term that applies to the flowering qualities of plants over multiple years. Thus, perennials are the correct classification for plants that return and bloom year after year.