A buffer resists pH change by holding a weak acid and its conjugate base together in the same solution. Add acid and the base mops it up; add base and the acid does. The pH that results is given by the Henderson-Hasselbalch equation.
pH = pKa + log₁₀([A⁻] ÷ [HA])
With equal concentrations of both, the log term is zero and the pH equals the pKa exactly. For acetic acid at pKa 4.76, the buffer pH calculator returns 4.76 with the solution half dissociated.
The ratio, not the amount
The equation depends on the ratio of base to acid rather than on how much of either is present. A two to one ratio gives pH 5.06, a 0.3 unit shift, whether the concentrations are 0.2 and 0.1 or 0.002 and 0.001.
That has a useful consequence and a dangerous one. The useful one is that diluting a buffer does not change its pH, which is why buffers are robust to small volume errors. The dangerous one is that the pH gives you no warning about how much capacity is left, because a buffer approaching exhaustion reads perfectly normal right up until it does not.
Watch what the shifts do
Start from 0.1 and 0.1 at pH 4.76 and convert 0.01 mol/L of the base into acid, as adding a strong acid would. The ratio becomes 0.09 to 0.11, and the pH falls to 4.67, a shift of 0.09 units. That is a buffer working.
Now convert 0.09 instead, leaving 0.01 against 0.19. The pH falls to 3.48, a shift of 1.28 units. Nine times as much acid produced fourteen times the pH movement, and the next increment after that would be worse again. The collapse is not gradual, because the log of a ratio approaching zero falls off a cliff.
Capacity has a number
The buffer capacity calculator puts a figure on it using the Van Slyke equation. For a 0.1 mol/L buffer at its pKa, the capacity is 0.0576 mol per litre per pH unit. One pH unit away it is 0.0190, a third of the peak. Two units away it is 0.0023, about a twenty-fifth.
That is the quantitative version of the usual advice to pick a buffer whose pKa is within one unit of your target pH. Outside that window you still have a solution containing a weak acid and its conjugate base, and it is no longer usefully buffering anything.
Capacity also scales with total concentration, so a 0.5 mol/L buffer at its pKa absorbs five times as much as a 0.1 mol/L one. Concentration buys capacity; the pKa match buys efficiency; and the pH tells you about neither.
For the underlying scale, see why pH is a logarithm, and for an unbuffered weak acid on its own there is weak acid and base pH.