This character is a Other Symbol and is commonly used, that is, in no specific script.
The glyph is not a composition. It has no designated width in East Asian texts. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. U+26C0 offers a line break opportunity at its position, except in some numeric contexts.
The Wikipedia has the following information about this codepoint:
Checkers (American English), also known as draughts (; British English), is a group of strategy board games for two players which involve forward movements of uniform game pieces and mandatory captures by jumping over opponent pieces. Checkers is developed from alquerque. The term "checkers" derives from the checkered board which the game is played on, whereas "draughts" derives from the verb "to draw" or "to move".
The most popular forms of checkers in Anglophone countries are American checkers (also called English draughts), which is played on an 8×8 checkerboard; Russian draughts and Turkish draughts, both on an 8x8 board; and International draughts, played on a 10×10 board – with the latter widely played in many countries worldwide. There are many other variants played on 8×8 boards. Canadian checkers and Malaysian/Singaporean checkers (also locally known as dam) are played on a 12×12 board.
American checkers was weakly solved in 2007 by a team of Canadian computer scientists led by Jonathan Schaeffer. From the standard starting position, perfect play by each side would result in a draw.