alpha-hydrogen acidity
Most C-H bonds are not acidic at all — methane has a pKa near 50, meaning its hydrogens essentially never leave as protons. Yet the hydrogen on the carbon next to a carbonyl is dramatically more acidic: the alpha-hydrogen of a ketone or aldehyde has a pKa around 19-20. That is still a weak acid (water is 15.7, acetic acid is 4.76), but it is about a trillion-trillion-trillion times more acidic than an ordinary C-H. That gap is the whole story.
Why so much more acidic? It is not the C-H bond itself but the stability of what is left behind. When you remove the alpha-proton, the negative charge does not sit stranded on carbon; it spreads onto the carbonyl oxygen through the adjacent pi-system. The resulting anion — the enolate — is resonance-stabilized, with the charge shared between the alpha-carbon and the oxygen. Oxygen is electronegative and happy to hold negative charge, so the anion is far more stable than a bare carbanion, and a more stable conjugate base means a stronger acid.
Put a carbon between TWO carbonyls and the effect doubles. A 1,3-diketone, a beta-keto ester, or malonic ester has a doubly-activated CH2 with a pKa around 9-13 — acidic enough to be fully deprotonated by mild bases like sodium ethoxide. This is the key that unlocks the malonic ester and acetoacetic ester syntheses: those very acidic protons can be removed cleanly, the carbon alkylated, and the helper carbonyl removed later by decarboxylation.
Compare pKa values: ethane ~50, acetone ~20, ethyl acetoacetate (a beta-keto ester) ~11, malonic ester ~13, and a 1,3-diketone like pentane-2,4-dione ~9. Each additional flanking carbonyl drops the pKa by roughly ten units.
One flanking carbonyl makes a proton acidic; two flanking carbonyls make it remarkably so.
A common error is to think the acidity comes from the C-H bond being weak in energy. It is really about resonance stabilization of the conjugate base (the enolate). The carbonyl oxygen, not the carbon, carries most of the negative charge in the most important resonance form.