Home Is Where the Burrow Is
The Burrow is described as a place mainly held up by magical means, containing so many bits and pieces that it couldn't possibly continue standing upright in any other way. In my opinion, this is just one of the facets that make it such a homey environment, perfect for Ron to call home and brilliant for giving the family that Harry thinks of as his own (and eventually marries into).
Though I'm sure we all have different interior design preferences and decorations we'd like to see, I've personally always felt most at home in slightly cluttered places. Places like the Burrow, that often contain trinkets special to the families that live there or that represent things the people there enjoy, allow a visitor to get to know the inhabitants better without words needing to be shared. Even when I find myself unfamiliar with the items, whether there's an overlying theme or not, it gives off the distinct feeling of being lived in.
The Burrow also has a charming landscape surrounding it with even more subtle insight to the family's interests and history. The front yard, with the Ford Anglia Arthur Weasley spent so long upgrading, and his subsequent shed filled with Muggle objects is quite charming to behold. There's no other feeling quite like watching someone talk about what they're passionate about, and seeing the things that inspire that passion is always a sight to behold. The back yard and surrounding property also tells a story. The broom closet, where all six Weasley boys kept their brooms that young Ginny would take out one at a time to practice on since they wouldn't let her join in, is just one example. Even the slightly annoying gnomes that frequent the back garden add a humorous nature to the home as a whole (even if in the end, they are in fact an extra chore).
One of the key factors that makes the Burrow such a home though is the people that live in it. The Weasley family, since it is so large, has so many personalities and so many activities going on that nothing is ever boring. Whether it's the sounds of explosions coming from Fred and George's shared room, a game of three-on-three Quidditch in the orchard, or a family dinner in the garden lovingly prepared by Molly Weasley, life at the Burrow is at full volume. And when the world is in the state it was when Harry was growing up, a home like that is one of the things he appreciated the most.