Great question! This is exactly what my research is about.
I’d say there’s 2 main things to think about, in terms of what our voices sound like.
One aspect to this is that we all have different bodies, and that includes the shape and size of the body parts that make our voices. These include our “voice box”, which makes the melody of the voice – it sits inside our throat and there are tissues stretched across it that vibrate to make sounds when we speak / sing / laugh. Those tissues have different sizes and shapes across different people, which can lead to differences in the pitch of the voice, for example. Differences between voices also include all the parts of our mouths that shape how we sound – the size of the mouth, the shape of the tongue, and so on. Where one guitar or piano might sound subtly different from another, so our voices can differ because of how they’re built!
The other very important aspect of sounding different from each other is about how we use our voices. Most of us learn to speak in childhood, and the way we learn speech will be strongly affected by the people around us – for example, our parents, caregivers, family and friends. So, we will have some sort of accent that reflects who we are. Also, as our personalities develop, some of that can be reflected in how we sound when we speak, in our tone of voice or the way we speak in certain situations. All these things come together to mean that your voice has qualities that are individual to you, just like your handwriting!