A quadrilateral with no parallel sides, two pairs of congruent sides, two lines of symmetry, and all vertices are convex.
A kite is a quadrilateral where one pair of adjacent sides is congruent, and the other pair of sides is congruent too.
It is tempting to simplify the wording and just say "two pairs of congruent adjacent sides," but that is not specific enough. A quadrilateral with exactly three congruent sides has "two pairs of congruent adjacent sides" but is not called a kite.
One property of kites is that at least one of the diagonals is a line of symmetry for the quadrilateral. If you fold the kite along that diagonal, the two halves will match up exactly.
Kites also have diagonals that are perpendicular to each other. (Think about the sticks you tie together to make a toy kite.)
At least one of the diagonals of a kite will cut it into two isosceles triangles.