Coronary circulation
This is purely an anatomical definition: right dominant is defined as coronary circulation where the PDA (posterior descending artery) is a branch of the RCA (right coronary artery) and left dominant is defined as coronary circulation where the PDA is a branch of the LCX (left circumflex artery). The Wikipedia article on coronary circulation is a reasonable reference for this question.

There's nothing else special about the statement "dominant" and it doesn't have any other importance for cardiac function, except that someone who is left dominant would have more serious issues if there is a blockage in their left main or LCX.

Typical human coronary artery anatomy consists of two ostia off the aorta, right and left. The "left main" branches fairly early on into the LAD (left anterior descending) artery, which follows the septum between left and right ventricles down the anterior side, and the LCX, which follows the 'top' of the left ventricle counter-clockwise (if looking down at the top of heart and rotating the heart so the atria are on top; in an actual human heart the atria actually point towards the midline a bit more than other species). The RCA travels in roughly mirror fashion, following the 'top' of the right ventricle in clockwise fashion. The RCA and LCX nearly meet on the other side of the heart, at the posterior septum.

In a majority of people, the RCA continues and follows the septum down to the apex (kind of like the LAD but on the opposite side). In a non-negligible minority, the supply of the posterior descending artery is either shared by RCA and LCX or is completely supplied by the LCX.