In ethylene, each carbon atom is sp² hybridized. In sp² hybrid orbitals the s-orbital is combined with two p orbitals to form 3 sp² orbitals. Meanwhile the 3^rd p orbital (here the p_zis conserved. The model below shows the atomic and hybrid orbitals of an sp² carbon. You can toggle the individual orbitals on and off with the buttons below.

The double bond is formed from two distinct bonds. One sp² orbital of each carbon are combined in phase to form a σ bond, as shown in the 3D model below. This σ bond is rotational symmetrical in the bond axis. Out of phase combination forms the antibonding σ* orbital.

The residual p orbitals of each carbon atom form the second bond. In phase overlap leads to a bonding π orbital, see 3D model below. This π orbital is not rotationally symmetrical around the bond axis, and therefore rotation around this bond is hindered as it would break the π bond. Out of phase addition produces the antibonding π* orbital.