It is a set phrase, and it means that your real home is not aways where you were born. Instead, your real home is the place that you feel the strongest emotions about, or where your heart is. There is another saying - "I left my heart in San Francisco". It means that someone has visited San Francisco and liked it so much that they have strong feelings toward it. So they say they "left their heart" there. Even though I now live in California and was born in a small town in Wisconsin, I feel like my real home is in another town in Milwaukee because that is where all of my best memories are. That's where my heart is. And since home is where your heart is, that must be my home. :)

I think it means that "home" isn't the house/apartment you live in but it's rather the place or person that makes you feel safe and warm inside. Of course you can feel like that while being at your house, but this phrase suggests that your "home" is with the person or in the place that you love most which doesn't have to be your house. So for example you could say: "I don't mind moving round the world with Sascha. Home is where the heart is." You'll feel at home with him no matter where you are, because he's your "home".