The orbit looks weird because the animation is from a viewpoint that is co-revolving with the Earth around the Sun. If the animation had been done using a fixed co-ordinate system (like using the vernal equinox as a fixed axis) you would have seen the Earth making its yearly trip around the Sun, with this asteroid staying roughly 60 degrees ahead of the Earth more-or-less along the Earth's orbit. This asteroid's orbit is not co-planar, so as it goes around the Sun, the asteroid drifts above and below the plane of the Earth's orbit, spending about 6 months 'below' and 6 months 'above' the Earth's orbit.

The mutual gravitation pull from the Sun and the Earth make these 'Trojan points' relatively stable orbital locations. The planet Jupiter has 2 large clusters of 'Trojan Asteroids', one group 60 degrees ahead of Jupiter and the other 60 degrees behind Jupiter in its orbit around the Sun.

In this animation, the loops that the asteroid makes are not perfect circles because neither the asteroid nor the Earth is in a circular orbit. The differences in orbital speed along their respective elliptical orbits is what gives the loops you see their odd shapes.

Cool video.