A clock position is the relative direction of an object described using the analogy of a 12-hour clock to describe angles and directions. One imagines a clock face lying either upright or flat in front of oneself, and identifies the twelve hour markings with the directions in which they point.
Using this analogy, 12 o'clock means ahead or above, 3 o'clock means to the right, 6 o'clock means behind or below, and 9 o'clock means to the left. The other eight hours refer to directions that are not directly in line with the four cardinal directions.
In aviation, a clock position refers to a horizontal direction; it may be supplemented with the word high or low to describe the vertical direction which is pointed towards your feet. 6 o'clock high means behind and above the horizon, while 12 o'clock low means ahead and below the horizon.
The 1949 movie Twelve O'Clock High takes its title from the system. In this case, the position would be ahead and above the horizon.
The phrase "on your six" refers to the system, six referring to the six o'clock or following position.