So my new stingray bass has 2 9V batteries in it, which people tell me is for more headroom, but as a newbie, I have no idea what that even means. I have noticed, compared to my other, cheap bass, that its definintely more crisp/clear. I have yet to experiment with all the different knobs etc too. My other question is there an instance where more headroom would be useful?
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Head room is that space between how far you have to turn the volume up on your equipment to do what you need to do and maxed out.
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Headroom is how much you have left over from where you plan to mostly play. If you walk through a room with taller ceilings, it doesn’t necessarily make your walk any better. If you start to jump, more headroom means you won’t hit your head. In this case jump means dig in, pick or slap. Arguably, it could allow cleaner and more articulated character to sharp transients.
However, if the next room you walk into doesn’t also have tall ceilings, the jumping is going to get stopped. In this case the next rooms may be pedals, DAI or amp and cabinet.
It could also be someone was able to design what they thought was a better active EQ and preamp circuit having an 18V swing available. Sometimes electronics work better if they aren’t working near their limits.
It’s one of the many fun choices you get to make with your ears!
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So it’s like being able to crank up the volume and not have feedback like you would otherwise?
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Thanks for the explanation 
That makes sense.
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Think of it like this. If your amps volume goes to 10 and you usually turn it up to 7 you have a headroom of three (so if you really dig in with a pick, or stomp on your distortion pedal, your amp can give you a little more volume without turning it up more). More headroom would mean you still play at 7 but your amp can now go to 12.
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Ahhh ok that makes sense too Thanks 
In the real world, in amps at least, it is one of the big reasons that people like to buy huge watt amps. Even though they won’t use the 1000w or whatever on a regular basis, and just keep the volume at a lower level, the argument is that if you hit some huge crescendo your amp has plenty of headroom to handle it. Also, In the real world, this is controversial and many sound engineers will call shenanigans on this. Your bass’s active electronics are the same concept: more volts equals more headroom so you will get more output out of your pickups if needed.
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I just have a fender rumble 15 and the BOSS GT1B bass processor. I don’t play in a band or anything, just at home for fun.
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Me too 
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I haven’t even had an amp at all for over a year
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When I was at the store trying out some basses, they hooked me up to a NICE amp. I think it was a Fender and it was a little over $1K but it was niiiice. If I was going to upgrade, that’s what I’d get. Although the GT1B has various amp settings to pick from so I doubt I’d need that. It was nice tho.
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Just keep in mind that the room your playing in does give a different sound/feeling of an amp. So that niiiice amp in store might be to sharp sounding at your place where you’re practicing.
I practice at home mostly in the living room (about 35m2) with an 15 watt Ashdown Tourbus. And it’s loud, yet if I take it to my ‘shed’ the official practice room, which has regular 60 watt amps from several brands, like Fender, Hartke (we rent that place), my tourbus is still loud enough, but sounds weak, not low.
A bit like jumping outside, plenty of headroom then.
That’s my reason to use severel amps and/or di-box when gigging. (And man I wish we could today, just do that gigging).
headroom is the dynamic range you have before the signal starts to clip.
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+1 to what everyone is saying here, and I think @terb made it the most succinct.
I have a bass with 2 9V batteries in it… It’s a 1995 Modulus, so we probably are talking about different electronics, but for my setup, I wouldn’t describe it as headroom. On my system, the batteries power and boost the onboard preamp for my pickups. I have a treble and bass control for the pickup - a preamp from the bass before it gets to the preamp on the amp.
The two 9V batteries can pack a massive punch. Rather than feeling like I had headroom, I always felt like it was just too damn loud for most amps. It sounded best when it was maxed out, but the amp had to have a serious pad on it (gain reduction) to allow for the super loud signal. It also really messed with it’s ability to sound good in pedals, because the signal coming in was so hot (when the pickups were maxed) it clipped the pedals.
So, headroom is great if the sound of the pickups with minimal preamp boost sounds good - but it can be frustrating if they sound best when they’re maxed, because not many amps/pedals can handle that much gain from the instrument.
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