The Laguz Stone can be thought of as the Path of Radiance and Radiant Dawn equivalent of the Dragonstones used by the Manaketes hailing from other titles in the series, their only difference being that Manaketes cannot transform without Dragonstones, whereas Laguz can without Laguz Stones.
In Radiant Dawn, using a Laguz Stone is counted as one action and will end the turn of the unit in question.