The origin of the checkered coat of arms is not clear. There is an early reference by a monk Fruhmun von Tegermsee in 1030-1050 A.D. It read that Svetoslav Shurin from Croatia had beaten Venetian doge Peter II in a game for the rights to govern the Dalmatian cities. The Coat of Arms can be found on a fond in split from the 11th century, in the wings from the eagles.
Also from the 11th century is the moravian Coat of Arms. Moravia is mentioned to be connected to Croats.
The croats had strong ties in the middle ages to the church and were very influentual. It is unknown if they are connected to the Conti family who delivered many popes. However it is remarkable that this family also has a checkered eagle as Coat of Arms (here from pope Innocentius III).
From left to right, they represent 5 regions:
1. Ancient Croatia: A gold 6-point star (morning star) over a crescent on a blue shield - thought of as an ancient Illyrian symbol and possibly the most ancient flag used by Croatians.
2. Republic of Dubrovnik: This region was once a republic in southern Dalmatia, specifically from 1358-1808. Two red stripes on a dark blue colored shield represent its coat-of-arms. Today, "Dubrovnik" represents the famous and ancient walled city.
3. Dalmatia: There is no "border" outlining exactly where Dalmatia lies, but it is generally a term outlining the central to southwestern coast of Croatia. Its shield is represented by three golden crowned leopards on a light blue background.
4. Istria: The peninsula on the northwestern end of Croatia, which has heavy Italian influence. Its crest is a golden goat with red horns.
5. Slavonia: This is the name for a region that encompasses much of eastern Croatia. Its coat include two silver stripes representing the north & south border. The furry creature in the middle is a marten (called "Kuna" in Croatian, which is also the name of the country's currency), with a 6-point gold star above it.