TBM: Ordnance Survey would establish
Bench Marks to mark a known elevation at a known point above sea level. A building firm is not concerned with sea level, but simply wants to map a small land area. So they can set a TBM from which all other measurements of the site can be made.
Backsight and foresight (Paragraph 4) is looking behind you to the last measured point, and ahead to the next point of interest respectively.
Collimation is making sure that the vertical axis of the theodolite is optically aligned to a true 90� to the horizontal.
HPC: Height of Plane of Collimation. This is the height of the instrument with which observations are being made. Take a backsight to the benchmark and staff as in the diagram shown in the backsight/foresight link. This will establish the height of the HPC. By taking a foresight to another point, and calculating the difference between the HPC height and the new measured height will give the height of the new point relative to the benchmark.
Took a while to write, and I see Karl's got in ahead of me!