Carbonyl compounds typically undergo enol/ketone tautomerism, i.e. for acetone we can write:
#H_3C-C(=O)CH_3rightleftharpoonsH_2C=C(-OH)CH_3#
This equilibrium lies strongly to the left, but it may be manipulated.
The alcohol, #"the enol"#, contains a protic hydrogen, that can be potentially deprotonated to give an enolate, the anion:
#H_2C=C(-OH)CH_3+"Base"rightleftharpoonsH_2C=C(-O^(-))CH_3+"Base"""^(-)H""^(+)"#
The enolate anion itself is conceived to be in equilibrium with the carbanion:
#H_2C=C(-O^(-))CH_3rightleftharpoonsH_2^(-)C-C(=O)CH_3#.
This #"carbanion/enolate"# equilibrium is the classic strategy employed in #C-C# bond formation. Carbanions may be formed from malonic acid derivatives, and ethylacetoacetate. For more details consult your organic text.