Asphalt and concrete seem to never pave enough surface, so there's always some mud on the sides. Trucks and tractors enter the roads from the fields without cleaning up their tires, or park on the side with right side wheels on the soft shoulder, which loses grass very fast if this repeats frequently. The sidawalks also follow the whims of urban planners, not the natural pedestrian paths, so many people just cut corners, literally.
The quality of the soil is also rather different than that in the US - it's black, the dust is much finer grained, and the mud is stickier. When the rain starts falling, the dust on the road and pavements forms a thin layer of almost liquid mud, which is also very slippery - beware when driving! This also means that the tires and soles are never exactly clean, except maybe in the very centers of larger cities. Anywhere else, chances are that you're carrying some of the planet in the grooves.
Two widespread customs arose from this: first, you don't walk around your home in your shoes. That's what the slippers are for. If you arrive to someone's place as a guest, you should at least make a bona fide attempt to get rid of your footwear in the lobby (predsoblje - literally, anteroom). Most people nowadays assume that you didn't really get in contact with mud, what with pavements being kept generally much cleaner than in previous decades, so they'll mostly persuade you to keep your shoes, but some may not. Be a good guest and offer to unshoe yourself, specially if you've checked your soles before entering and found them populated.
The other custom is that even if you have your shoes on while you're inside, you never ever lift them on furniture. The floors being much easier to clean nowadays, your host (or landlord, for that matter) may not care that some dust will have to be cleaned up, but cleaning the sofas, armchairs, couches and especially beds is much harder to do. I've even been asked to explain how come that they see Americans get on their beds with shoes still on - it's something nobody here can understand.