It is similar to the more commonly encountered aspis in that it has an overall circular shape, but differed in having scooped indentations at both sides.
A Greek phalanx was a military unit whose performance was based in part on the relative uniformity of arms and armor of its principal members, the hoplites.
This need for uniformity apparently extended to the shape of the groups' shields.
[1] The Boeotian shield was narrower and more oval than the circular aspis, and on each of its vertical edges was a scooped indentation not unlike the C-bouts found on the waist of a modern violin and probably used for similar purpose: just as the violin's C-bouts allow the player to run the bow close to the center of the instrument, the Boeotian shield's indentations allowed its bearer to thrust and stab with his weapon(s) from a position closer to the shield's center rather than having to reach around or over the shield to strike.
It is also possible that the Boeotian shield was constructed out of animal hides stretched over a wicker frame rather than being made of solid wood and bronze like the aspis— this would account for none from the ancient world having survived.