Townships
Shown below - sixty-four Townships, with Base Line, and Meridians:

Each extension of the PLSS begins at an initial point established as a control point for the survey.  A north-south line through the initial point is called the Principal Meridian, and an east-west line through the initial point is the Base Line.  There are thirty-three Initial Points with principal meridians and base lines in the contiguous U.S., and five in Alaska.

Meridians and base lines act as the reference axis for the rest of the survey.  Township lines are township boundaries running east and west and are intended to be true parallels of latitude.  Range lines are township boundaries running north and south and are intended to be true meridians of longitude.

Because of the curvature of the earth, the convergence of township lines increases the farther north they extend.  So the PLSS establishes standard parallels typically every 24 miles north and south, i.e. every four townships.  Working along principal meridians and base lines surveyors set corners every ½ mile, and establish township corners at six mile intervals.

PLSS Subdivisions
Each township is divided into thirty-six one mile square sections, as shown below.

Sections can be further subdivided, into quarter sections, quarter-quarter sections, and smaller.  Aliquot parts are legal subdivisions of a section, except (government) lots, or further subdivision of any smaller legal subdivision, except (government) lots, by division into halves or fourths ad infinitum.  "Aliquot" means "contained in something else an exact number of times."