Carbon negative is an adjectival phrase used to describe any process that removes carbon dioxide from the atmosphere, with the intent to avoid global warming.
A carbon dioxide sink such as a concentrated group of plants or algae or any other primary producer that binds carbon dioxide into biomass - as with forests and kelp beds - is not carbon negative but carbon neutral. A carbon dioxide sink of this type moves carbon, in the form of carbon dioxide, from the atmosphere or hydrosphere to the biosphere. That carbon will return to the atmosphere or hydrosphere in the form of carbon dioxide as a part of the carbon cycle.
Carbon dioxide sinks that store carbon dioxide in the Earth's crust by injecting it into the subsurface, or in the form of insoluble carbonate salts (mineral sequestration), are considered carbon negative. This is because they are removing carbon from the atmosphere and sequestering it indefinitely and presumably for a considerable duration (thousands to millions of years).