the 2000s (decade 2000-2009); the '00s; the aughts; the noughties
Refers specifically to the ten-year period from 2000 to 2009. In Japanese, 年代 usually means a decade.
Music from the 2000s is still popular today.
Can refer to the entire 21st century when context makes it clear, though ２１世紀 is more common for the century.
the 2000s (millennium 2000-2999)
Rarely used for the entire millennium; usually ２０００年代 means the decade. This sense appears mainly in futuristic or historical contexts.
This technology will develop throughout the 2000s.
In the distant 2000s, humanity may have expanded into space.