Vaquero refers to generally to a "cowboy" but more specifically to a herdsman or cattleman. The vaqueros of Antonion's father's generation moved cattle from place to place across the vast open spaces of Texas and the wider southwest.
The term for those open spaces is "llano", which means planes.
Antonio's father longs always to return to the type of freedom he associates with herding cattle across the southwestern planes. He feels that in movement there is freedom and fulfillment. However, after seeing his three oldest sons claimed by that desire for movement and freedom - and losing them to that desire, Gabriel begins to feel differently about these impulses.
". . . Every generation, every man is a part of his past. He cannot escape it, but he may reform the old materials, make something new."