Hybrids are essentially, for lack of a better term, kemonomimi.
They are a cross between human and another living creature. (ex. Bird, Mammal, Fish, Plant, etc.) Their genes are split about half and half, leaving both human and 'animal' traits, both physical and otherwise.
While humans are capable of most or all magics, hybrids are only able to properly use one. This one magic is the transformative shapeshifting magic that allows select hybrids to transfer between their human, hybrid, and 'animal' forms respectively. However, not all hybrids have this magic.
While some members may disagree, the majority of the human population of Soliciem harbors no prejudice against hybrids and vice versa. They are treated equally and without distain by most people. However, select groups do find hybrids not to their liking or have a disdain for them altogether. (See: Soralia)