If decibels are a ratio, what is 0 dB measured against in a digital audio editor, and why is everything below it negative?

What does 0 dB actually mean in digital audio?

In a digital editor, 0 dB is full scale — the largest number the format can represent. There is nothing above it, which is why every level you see is negative and why exceeding it clips rather than getting louder. The same figure means different things elsewhere, and that is the source of the confusion.

Why it is a ceiling and not a midpoint

The decibel is a ratio, so it needs a reference, and in the digital domain that reference is the maximum value the samples can hold. One answer made the consequence concrete: a 16-bit file and a 24-bit file have very different numbers of available levels, but full scale is full scale in both, so 0 dB sits at the top of each. The extra bits buy resolution below the ceiling, not headroom above it.

The three meanings people run into

Digital full scale. The loudest representable signal. Everything below reads as a negative number, down towards silence.
Unity, on a mixer or a plugin. Here 0 dB means no change: below it reduces the signal, above it applies gain. This is the reading that makes 0 dB a middle rather than a maximum.
Sound pressure level, where 0 dB is referenced to the threshold of human hearing rather than to anything in your project.
One answer made the general point plainly: unless the unit is qualified, the reference is open to interpretation, which is why the same number appears to contradict itself across tools.

What it means when you are working

On a meter, 0 dB is the limit. Going past it does not make the signal louder, it clips.
Leave headroom below it. One answer noted that when a system quotes an ideal operating level, there is deliberately room above that point before clipping.
The behaviour is the same in digital and analogue mixing: below unity reduces, above unity adds gain.
Check the documentation for the specific meter you are reading, because implementations differ about whether the mark is the maximum or the intended target.

Where the unit came from

The accepted answer traced it back further than the question asked, and it explains the shape of the thing. Logarithms exist to turn multiplication and division into addition and subtraction, which mattered enormously before calculators. Working in decibels is what that convenience looks like when it is applied to audio levels — which is why gain changes add up rather than multiply, and why the scale compresses an enormous range into readable numbers.