if your noise floor is at say -85 db, then sounds quieter than that will be obsured by noise. if you max at zero, then you will have a dynamic range of 85 db. if you max at +15, you will have a dynamic range of 100 db, and you will be able to raise some of your quietest sounds above the noise floor.

but you are right as well, it will also have a louder peaks and overall rms level.

the thing about dbs is that they are relative, not absolute. so once the sound comes into a digital device, everything changes. ie, my motu can take a +19 db signal coming in, but once inside the computer, that same signal would read 0 db. if i record at +10, the recording actually comes out as -9, and requires boosting inside the computer, etc.