As others have said, the inner child is an incredibly useful metaphor for trauma/therapy. The way your brain reacts to trauma is to basically create a bookmark of you at that time. If you manage to live through the trauma, then clearly, the emotions you felt and the actions you took worked perfectly!
Well, that was probably true in prehistory, but nowadays it's a big fucking stupid liability. Like, for example, say I'm doing my adult job at $company and my coworker Todd Fuckwit (esq.) says something shitty about suicide that reminds my brain of an old bookmark. All of the sudden, my emotional state is transported back to when Young Badabinski saw the results of a parental suicide attempt and thought it was entirely their fault and Badabinski deserved it (Important note, this is not regular PTSD with vivid hallucinations/flashbacks, this is more about emotions). Now I'm freaking out in the meeting room and abruptly leave because I feel like a 12 year old who has just had their world ended, and escaping us what I did back then.
The way you heal this is to try to create a connection with that bookmark of yourself and then give yourself what you needed back then. Over many therapy sessions, I was able to help young Badabinski realize that none of that was their fault, that they didn't deserve to see that, and that they should have had the warm and loving care of both of their parents. And you know what? It really fucking worked.
For more chronic cases (like a lot of emotional neglect), your inner child is just kinda... There? Like, the bookmark part of the metaphor breaks down a bit. Your inner child represents the tender emotions that were left unhandled and childhood needs that were left unmet. A lot of my therapy nowadays is helping my inner child feel less deprived and more loved on a day-to-day basis, because if I don't take care of myself enough in the ways I need, then my brain will pull up the chronic inner child and I'll be miserable for days/weeks/months. In contrast, the parts of my life where I've permanently changed my day-to-day behavior feel so much more fulfilling and wonderful. It's not just about avoiding the negatives, you end up focusing more on achieving the positive.
I personally like describing it as a metaphor. I was a bit of an angry skeptic when I was younger (due to the aforementioned parent moving to a bunch of new-age crystal healing shit after their recovery and then trying to push it on me when I absolutely did not believe in the validity of those methods), so I didn't like how metaphysical and "touchy-feely" an inner child felt. I'm no longer skeptical of this idea am a much more emotionally liberated person. I often think of my inner child as if it were an active presence in my mind (it feels more effective to do so for me). It took a lot of time time for me to reach that place. I believe that explaining it as a metaphor will get through to people who would otherwise spurn the concept. Metaphor or not, I still want to help the little human that is past me, and I'd love to be able to drink a potion that would let me talk to that twelve year old.