I don't know if my significant others have ever "understood" it, but they have accepted it.
I think the major differences with horses is that it's a hobby that changes your lifestyle.
I don't know if it's possible to explain, other than saying that this is simply part of who you are. It's not an addition to your life but it is your life.
I think ways to make it work are to try to leave the horse stuff at the stable. Don't come home complaining about a ride, or have a car full of hay, plod around in your tall boots and breeches. Leave the horse stuff at the horse. Outside of the horse be a "normal" person.
Saying all that I don't know if I could make it work long term with someone who wasn't pretty "open" to horsey stuff. Part of my life plans are to buy a small property, have animals etc. I value animals, outdoors, open spaces, the quiet, genuine country type people - these aren't things I'd be willing to give up. I grew up as a city kid, and I know even if I liked some of the people from the city a lot of them just wouldn't have the same goals or ideals as me.