Being that planets don't have their own propulsion systems, where does the energy come from to produce Milankovitch cycles?
In astronomy and astrophysics, when the question is, "where does the energy come from?" often the answer is, "gravity." This is the case with Milankovitch cycles as well. Milankovitch cycles describe variations in the Earth's orbit, specifically variations in eccentricity, axial tilt, and precession.
Eccentricity is a measure of how elliptical a planets orbit is. An eccentricity of 0 would be a perfectly circular orbit, and a higher eccentricity would look like a comet's orbit.
Axial tilt, or obliquity, is a measure of how far the rotational axis of the Earth is off from perpendicular to its orbital plane. If we were to look at the Earth's orbit edge on, an axial tilt of 0 would have the Earth's orbital axis straight up and down.
Because the Earth does have some axial tilt, it experiences precession, where the axis rotates like a top spinning off center. While eccentricity and axial tilt are primarily effected by variations in the gravitational pull of the other planets, precession is mostly caused by the pull of the Sun and moon, and therefore would likely be the only significant cycle if the other planets didn't exist.