alpha-hydrogen atom and keto-enol tautomerism
In general, the "alpha" hydrogen is a hydrogen attached to a carbon that is "alpha" (adjacent to) the substituent.  



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So in this case, an "alpha" hydrogen is a hydrogen attached to the carbon alpha to the carbonyl.



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The following drawing represents a typical keto-enol equilibrium.  If we removed the last alpha hydrogen and replaced it with a substituent (alkyl group, phenyl group, bromine, etc.) then we could not form a double bond with that alpha carbon, it would have 4 non-removable substituents.  If we can't form a double bond that means we can't form an enol.



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