Here you can see the relationship between Signal-to-Noise
Ratio (SNR), the dynamic range and headroom.
Every audio-passing system (analogue or digital) has two limits: at the quiet end there is the noise floor, normally a constant background hiss into which signals can be faded until they become inaudible; and at the loud end there is clipping, the point where the system can no longer accommodate an increase in signal level and gross distortion results. The latter is generally due to the signal level approaching the power supply voltage levels in analogue systems, or the coding format running out of numbers to count more quantizing levels in digital systems.
Obviously, we need to keep the signal level somewhere between these two extremes to maximize quality: somewhere well above the noise floor but comfortably below the clipping point. In analogue systems, this is made practical and simple by defining a nominal working level and encouraging people to stick to that by scaling the meters in a suitable way. For example, VU meters are scaled so that 0VU usually equates to +4dBu. The clipping point in professional analogue gear is typically around +24dBu, so around 20dB higher than the nominal level indicated on the VU meter.
That 20dB of available (but ideally unused) dynamic-range space is called the headroom, or is referred to as the headroom margin. It provides a buffer zone to accommodate unexpected transients or loud sounds without risking clipping. It’s worth noting that no analogue metering system displays much of the headroom margin. Rather, it’s an ‘unseen’ safety region that is easy to overlook and take for granted. In most digital systems, the metering tends to show the entire headroom margin, because the meter is scaled downwards from the clipping point at 0dBFS. The top 20dB or so of a digital scale is showing the headroom margin that is typically invisible on the meters of analogue systems. As a result, many people feel they are ‘under-recording’ on digital systems if they don’t peak their signals well up the scale, when in fact they are actually over-recording and at far greater risk of transient distortion.
The reason why your interface offers greater headroom when operating from its external power supply is because the PSU provides a higher-voltage power rail than is possible when the unit is running from the USB power supply. A higher supply voltage means that a large signal voltage can be accommodated; in this case, twice as large, hence the 6dB greater headroom margin. More headroom means you have to worry less about transient peaks causing clipping distortion, and generally translates to a more open and natural sound, so it’s a good thing.